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Volumn , Issue , 2014, Pages 1-480

Diffusions, Markov processes, and martingales: Volume 2: Itô Calculus

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EID: 84953252414     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511805141     Document Type: Book
Times cited : (191)

References (389)
  • 2
    • 84990553776 scopus 로고
    • Brownian motion and the Harnack inequality for Schrödinger operators
    • AIZENMANN, M. and SIMON, B. Brownian motion and the Harnack inequality for Schrödinger operators, Comm. Pure and Appl. Math., 35, 209-273 (1982).
    • (1982) Comm. Pure and Appl. Math , vol.35 , pp. 209-273
    • Aizenmann, M.1    Simon, B.2
  • 5
    • 0000044071 scopus 로고
    • Stopping times and tightness
    • ALDOUS, D. Stopping times and tightness, Ann. Prob., 6, 335-40 (1978).
    • (1978) Ann. Prob , vol.6 , pp. 335-340
    • Aldous, D.1
  • 6
    • 84953227521 scopus 로고    scopus 로고
    • Negatively curved manifolds, elliptic operators and Martin boundary (to appear)
    • ANCONA, A. Negatively curved manifolds, elliptic operators and Martin boundary (to appear).
    • Ancona, A.1
  • 9
    • 4244023428 scopus 로고
    • Temps locaux
    • Société Mathématique de France
    • AZEMA, J. and YOR, M. (Editors) Temps locaux, Astérisque 52-53, Société Mathématique de France, 1978.
    • (1978) Astérisque , pp. 52-53
    • Azema, J.1    Yor, M.2
  • 11
    • 0039488440 scopus 로고
    • Study of a filtration expanded to include an honest time
    • BARLOW, M. T. Study of a filtration expanded to include an honest time, Z. Wahrscheinlichkeitstheorie, 44, 307-323 (1978).
    • (1978) Z. Wahrscheinlichkeitstheorie , vol.44 , pp. 307-323
    • Barlow, M.T.1
  • 13
    • 0001109252 scopus 로고
    • One dimensional stochastic differential equation with no strong solution
    • BARLOW, M. T. One dimensional stochastic differential equation with no strong solution, J. London Math. Soc., 26, 335-347 (1982).
    • (1982) J. London Math. Soc , vol.26 , pp. 335-347
    • Barlow, M.T.1
  • 15
    • 84963019945 scopus 로고
    • Inequalities for a pair of processes stopped at a random time
    • BARLOW, M. T., JACKA, S. and YOR, M. Inequalities for a pair of processes stopped at a random time, Proc. London Math. Soc., 52, 142-172 (1986).
    • (1986) Proc. London Math. Soc , vol.52 , pp. 142-172
    • Barlow, M.T.1    Jacka, S.2    Yor, M.3
  • 16
    • 84953221402 scopus 로고
    • Inégalities pour un couple de processus arreˆtés à un temps quelconque
    • BARLOW, M. T., JACKA, S. and YOR, M. Inégalities pour un couple de processus arreˆtés à un temps quelconque, C. R. Acad. Sei., 299, 351-354 (1984).
    • (1984) C. R. Acad. Sei , vol.299 , pp. 351-354
    • Barlow, M.T.1    Jacka, S.2    Yor, M.3
  • 17
    • 0021442104 scopus 로고
    • One-dimensional stochastic differential equations involving a singular increasing process
    • BARLOW, M. T. and PERKINS, E. One-dimensional stochastic differential equations involving a singular increasing process, Stochastics, 12, 229-249 (1984).
    • (1984) Stochastics , vol.12 , pp. 229-249
    • Barlow, M.T.1    Perkins, E.2
  • 19
    • 0013468471 scopus 로고
    • (Semi-) martingale inequalities and local times
    • BARLOW, M. T. and YOR, M. (Semi-) martingale inequalities and local times, Z. Wahrscheinlichkeitstheorie, 55, 237-254 (1981).
    • (1981) Z. Wahrscheinlichkeitstheorie , vol.55 , pp. 237-254
    • Barlow, M.T.1    Yor, M.2
  • 20
    • 0038940556 scopus 로고
    • Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma and applications to local times
    • BARLOW, M. T. and YOR, M. Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma and applications to local times, J. Fund. Anal., 49, 198-229 (1982).
    • (1982) J. Fund. Anal , vol.49 , pp. 198-229
    • Barlow, M.T.1    Yor, M.2
  • 21
    • 0010163433 scopus 로고
    • The Malliavin calculus for pure jump processes and applications to local time
    • BASS, R. and CRANSTON, M. The Malliavin calculus for pure jump processes and applications to local time, Ann. Prob., 14, 490-532 (1986).
    • (1986) Ann. Prob , vol.14 , pp. 490-532
    • Bass, R.1    Cranston, M.2
  • 22
    • 0039458371 scopus 로고
    • Asymptotic behaviour of stochastic flows of diffeomorphisms; two case studies
    • BAXENDALE, P. Asymptotic behaviour of stochastic flows of diffeomorphisms; two case studies, Probab. Th. Rel. Fields, 73, 51-85 (1986).
    • (1986) Probab. Th. Rel. Fields , vol.73 , pp. 51-85
    • Baxendale, P.1
  • 25
    • 0002780103 scopus 로고
    • Brownian motions on the diffeomorphism group, I
    • BAXENDALE, P. Brownian motions on the diffeomorphism group, I, Compos. Math., 53,19-50 (1984).
    • (1984) Compos. Math , vol.53 , pp. 19-50
    • Baxendale, P.1
  • 26
    • 84953225388 scopus 로고    scopus 로고
    • Paper on Lyapunov exponents (to appear)
    • BAXENDALE, P. and STROOCK, D. W. Paper on Lyapunov exponents (to appear).
    • Baxendale, P.1    Stroock, D.W.2
  • 28
  • 29
    • 0000045348 scopus 로고
    • Systèmes de Lévy des processus de Markov
    • BENVENISTE, A. and JACOD, J. Systèmes de Lévy des processus de Markov, Invent. Math., 21, 183-198 (1973).
    • (1973) Invent. Math , vol.21 , pp. 183-198
    • Benveniste, A.1    Jacod, J.2
  • 30
    • 84968510898 scopus 로고
    • Local times and sample function properties of stationary Gaussian processes
    • BERMAN, S. M. Local times and sample function properties of stationary Gaussian processes, Trans. Amer. Math. Soc., 137, 277-300 (1969).
    • (1969) Trans. Amer. Math. Soc , vol.137 , pp. 277-300
    • Berman, S.M.1
  • 31
    • 84968521981 scopus 로고
    • Harmonic analysis of local times and sample functions of Gaussian processes
    • BERMAN, S. M. Harmonic analysis of local times and sample functions of Gaussian processes, Trans. Amer. Math. Soc., 143, 269-281 (1969).
    • (1969) Trans. Amer. Math. Soc , vol.143 , pp. 269-281
    • Berman, S.M.1
  • 32
    • 0000111128 scopus 로고
    • Gaussian processes with stationary increments: Local times and sample function properties
    • BERMAN, S. M. Gaussian processes with stationary increments: local times and sample function properties, Ann. Math. Statist., 41, 1260-1272 (1970).
    • (1970) Ann. Math. Statist , vol.41 , pp. 1260-1272
    • Berman, S.M.1
  • 33
    • 0346199076 scopus 로고
    • Stochastic integration and ZAtheory of semi-martingales
    • BICHTELER, K. Stochastic integration and ZAtheory of semi-martingales, Ann. Prob., 9, 49-89 (1981).
    • (1981) Ann. Prob , vol.9 , pp. 49-89
    • Bichteler, K.1
  • 35
    • 0000412091 scopus 로고
    • Calcul de Malliavin pour les diffusions avec sauts: Existence d’une densité dans le cas unidimensionnel
    • Springer, Berlin
    • BICHTELER, K. and JACOD, J. Calcul de Malliavin pour les diffusions avec sauts: Existence d’une densité dans le cas unidimensionnel, Séminaire de Probabilités X VII: Lecture Notes in Mathematics 986, Springer, Berlin, 1983, pp. 132-157.
    • (1983) Séminaire de Probabilités X VII: Lecture Notes in Mathematics 986 , pp. 132-157
    • Bichteler, K.1    Jacod, J.2
  • 38
    • 71549139003 scopus 로고
    • Conditional distributions and tightness
    • BILLINGSLEY, P. Conditional distributions and tightness, Ann. Prob., 2, 480-485 (1974).
    • (1974) Ann. Prob , vol.2 , pp. 480-485
    • Billingsley, P.1
  • 39
    • 84953308024 scopus 로고    scopus 로고
    • On fluctuation theory in higher dimensions
    • BINGHAM, N. H. and DONEY, R. A. On fluctuation theory in higher dimensions.
    • Bingham, N.H.1    Doney, R.A.2
  • 42
    • 34250245856 scopus 로고
    • Martingales, the Malliavin calculus and hypoellipticity under general Hörmander’s conditions
    • BISMUT, J.-M. Martingales, the Malliavin calculus and hypoellipticity under general Hörmander’s conditions, Z. Wahrscheinlichkeitstheorie, 56, 469-505 (1981).
    • (1981) Z. Wahrscheinlichkeitstheorie , vol.56 , pp. 469-505
    • Bismut, J.-M.1
  • 43
    • 84953247346 scopus 로고
    • Calcul de variations stochastiques et processus de sauts
    • BISMUT, J.-M. Calcul de variations stochastiques et processus de sauts, Z. Wahrscheinlichkeitstheorie, 56, 469-505 (1983).
    • (1983) Z. Wahrscheinlichkeitstheorie , vol.56 , pp. 469-505
    • Bismut, J.-M.1
  • 44
    • 0003203464 scopus 로고
    • Large deviations and the Malliavin calculus
    • Birkhauser, Boston
    • BISMUT, J.-M. Large deviations and the Malliavin calculus, Progress in Math., Birkhauser, Boston, 1984.
    • (1984) Progress in Math
    • Bismut, J.-M.1
  • 45
    • 0002876396 scopus 로고
    • The Atiyah-Singer theorems; a probabilistic approach: I, The index theorem
    • BISMUT, J.-M. The Atiyah-Singer theorems; a probabilistic approach: I, The index theorem, J. Fund. Anal., 57, 56-98 (1984).
    • (1984) J. Fund. Anal , vol.57 , pp. 56-98
    • Bismut, J.-M.1
  • 46
    • 0000490351 scopus 로고
    • Diffusions conditionnelles, I, II
    • 45,274-292(1981)
    • BISMUT, J.-M. and MICHEL, D. Diffusions conditionnelles, I, II, J. Fund. Anal., 44,174-211 (1981); 45,274-292(1981).
    • (1981) J. Fund. Anal , vol.44 , pp. 174-211
    • Bismut, J.-M.1    Michel, D.2
  • 47
    • 0007093484 scopus 로고
    • The Martin boundary for Polya’s urn scheme and an application to stochastic population growth
    • BLACKWELL, D. and KENDALL, D. G. The Martin boundary for Polya’s urn scheme and an application to stochastic population growth, J. Appl. Prob., 1, 284-296 (1964).
    • (1964) J. Appl. Prob , vol.1 , pp. 284-296
    • Blackwell, D.1    Kendall, D.G.2
  • 49
    • 0004256573 scopus 로고
    • Addison-Wesley, Reading, Mass
    • BREIMAN, L. Probability, Addison-Wesley, Reading, Mass., 1968.
    • (1968) Probability
    • Breiman, L.1
  • 51
    • 0039279315 scopus 로고
    • Topologie générale
    • Hermann, Paris, Chap. IX, 2nd edition
    • BOURBAKI, N. Topologie générale, in Eléments de Mathématique, Hermann, Paris, 1958, Chap. IX, 2nd edition.
    • (1958) Eléments de Mathématique
    • Bourbaki, N.1
  • 53
    • 0002455942 scopus 로고
    • Distribution function inequalities for martingales
    • BURKHOLDER, D. Distribution function inequalities for martingales, Ann. Prob., I, 19-42 (1973).
    • (1973) Ann. Prob , vol.1 , pp. 19-42
    • Burkholder, D.1
  • 54
    • 0001931654 scopus 로고
    • Conservative diffusions
    • CARLEN, E. A. Conservative diffusions, Comm. Math. Phys., 94, 293-315 (1984).
    • (1984) Comm. Math. Phys , vol.94 , pp. 293-315
    • Carlen, E.A.1
  • 55
    • 0000117704 scopus 로고
    • Potential scattering in quantum mechanics
    • BURKHOLDER, D. Potential scattering in quantum mechanics, Ann. Inst. H. Poincaré, 42, 407-428 (1985).
    • (1985) Ann. Inst. H. Poincaré , vol.42 , pp. 407-428
    • Burkholder, D.1
  • 56
    • 0007837893 scopus 로고
    • Flows of stochastic dynamical systems: Ergodic theory
    • CARVERHILL, A. P. Flows of stochastic dynamical systems: ergodic theory, Stochastics, 14, 273-318 (1985).
    • (1985) Stochastics , vol.14 , pp. 273-318
    • Carverhill, A.P.1
  • 57
    • 0007837893 scopus 로고
    • A formula for the Lyapunov exponents of a stochastic flow. Application to a perturbation theorem
    • CARVERHILL, A. P. A formula for the Lyapunov exponents of a stochastic flow. Application to a perturbation theorem, Stochastics, 14, 209-226 (1985).
    • (1985) Stochastics , vol.14 , pp. 209-226
    • Carverhill, A.P.1
  • 60
    • 0040452862 scopus 로고
    • Flows of stochastic dynamical systems; the functional analytic approach
    • CARVERHILL, A. P. and ELWORTHY, K. D. Flows of stochastic dynamical systems; the functional analytic approach, Z. Wahrscheinlichkeitstheorie, 65, 245-268 (1983).
    • (1983) Z. Wahrscheinlichkeitstheorie , vol.65 , pp. 245-268
    • Carverhill, A.P.1    Elworthy, K.D.2
  • 61
    • 4243219284 scopus 로고
    • La condition d’hypoellipticité d’Hôrmander
    • CHALEYAT-MAUREL, MIREILLE La condition d’hypoellipticité d’Hôrmander, Astérisque, 84-85, 189-202 (1981).
    • (1981) Astérisque
    • Chaleyat-Maurel, M.1
  • 65
    • 0007773356 scopus 로고
    • Probabilistic approach in potential theory to the equilibrium problem
    • CHUNG, K. L. Probabilistic approach in potential theory to the equilibrium problem, Ann. Inst. Fourier, Grenoble, 23, 313-322 (1973).
    • (1973) Ann. Inst. Fourier, Grenoble , vol.23 , pp. 313-322
    • Chung, K.L.1
  • 66
    • 0007019203 scopus 로고
    • Excursions in Brownian motion
    • CHUNG, K. L. Excursions in Brownian motion, Ark. Mat., 14, 155-177 (1976).
    • (1976) Ark. Mat , vol.14 , pp. 155-177
    • Chung, K.L.1
  • 67
    • 0042735148 scopus 로고
    • The condenser problem
    • CHUNG, K. L. and GETOOR, R. K. The condenser problem, Ann. Prob., 5, 82-86 (1977).
    • (1977) Ann. Prob , vol.5 , pp. 82-86
    • Chung, K.L.1    Getoor, R.K.2
  • 68
    • 0009203062 scopus 로고
    • To reverse a Markov process
    • CHUNG, K. L. and WALSH, J. B. To reverse a Markov process, Acta Math., 123, 225-251 (1969).
    • (1969) Acta Math , vol.123 , pp. 225-251
    • Chung, K.L.1    Walsh, J.B.2
  • 71
    • 84968478877 scopus 로고
    • First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path
    • CIESIELSKI, Z. and TAYLOR, S. J. First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path, Trans. Am. Math. Soc., 103, 434-450 (1962).
    • (1962) Trans. Am. Math. Soc , vol.103 , pp. 434-450
    • Ciesielski, Z.1    Taylor, S.J.2
  • 74
    • 0000855448 scopus 로고
    • The representation of functionals of Brownian motion by stochastic integrals
    • 42, 1778 (1971)
    • CLARK, J. M. C. The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Stat., 41, 1282-1295 (1970); 42, 1778 (1971).
    • (1970) Ann. Math. Stat , vol.41 , pp. 1282-1295
    • Clark, J.M.C.1
  • 75
    • 0012983624 scopus 로고
    • An introduction to stochastic differential equations on manifolds
    • (eds. D. Q. May ne and R. W. Brockett), Reidel, Dordrecht
    • CLARK, J. M. C. An introduction to stochastic differential equations on manifolds, in Geometric Methods in Systems Theory (eds. D. Q. May ne and R. W. Brockett), Reidel, Dordrecht, 1973.
    • (1973) Geometric Methods in Systems Theory
    • Clark, J.M.C.1
  • 76
    • 0001424885 scopus 로고
    • The design of robust approximations to the stochastic differential equations of nonlinear filtering
    • (ed. J. Skwirzynski), Sijthoff and Noordhoff, Alphen an den Rijn
    • CLARK, J. M. C. The design of robust approximations to the stochastic differential equations of nonlinear filtering, in Communication Systems and Random Process Theory (ed. J. Skwirzynski), Sijthoff and Noordhoff, Alphen an den Rijn, 1978.
    • (1978) Communication Systems and Random Process Theory
    • Clark, J.M.C.1
  • 79
    • 84953215276 scopus 로고    scopus 로고
    • Means of approach of two-dimensional Brownian motion
    • CRANSTON, M. Means of approach of two-dimensional Brownian motion (to appear in Ann. Probab.).
    • Ann. Probab
    • Cranston, M.1
  • 80
    • 0040560238 scopus 로고
    • Non-standard measure theory and its applications
    • CUTLAND, N. Non-standard measure theory and its applications, Bull. London Math. Soc., 15, 529-589 (1983).
    • (1983) Bull. London Math. Soc , vol.15 , pp. 529-589
    • Cutland, N.1
  • 83
    • 0000573290 scopus 로고
    • Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
    • DAVIES, E. B. and SIMON, B. Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Fund. Anal. 59, 335-395 (1984).
    • (1984) J. Fund. Anal , vol.59 , pp. 335-395
    • Davies, E.B.1    Simon, B.2
  • 84
    • 84968468705 scopus 로고
    • Picard’s theorem and Brownian motion
    • DAVIES, B. Picard’s theorem and Brownian motion, Trans. Amer. Math. Soc., 213, 353-362 (1975).
    • (1975) Trans. Amer. Math. Soc , vol.213 , pp. 353-362
    • Davies, B.1
  • 85
    • 0001610264 scopus 로고
    • On a multiplicative functional transformation arising in non-linear filtering theory
    • DAVIS, M. H. A. On a multiplicative functional transformation arising in non-linear filtering theory, Z. Wahrscheinlichkeitstheorie, 54, 125-139 (1980).
    • (1980) Z. Wahrscheinlichkeitstheorie , vol.54 , pp. 125-139
    • Davis, M.H.A.1
  • 87
    • 84953258154 scopus 로고    scopus 로고
    • Some current issues in stochastic control theory
    • DAVIS, M. H. A. Some current issues in stochastic control theory, Stochastics.
    • Stochastics
    • Davis, M.H.A.1
  • 88
    • 0000649234 scopus 로고
    • Dynamic programming conditions for partially observed stochastic systems
    • DAVIS, M. H. A. and VARAIYA, P. Dynamic programming conditions for partially observed stochastic systems, SIAM J. Control, 11, 226-261 (1973).
    • (1973) SIAM J. Control , vol.11 , pp. 226-261
    • Davis, M.H.A.1    Varaiya, P.2
  • 89
    • 0001356070 scopus 로고
    • Large deviations from the McKean-Vlasov limit for weakly-interacting diffusions
    • DAWSON, D. A. and GÄRTNER, J. Large deviations from the McKean-Vlasov limit for weakly-interacting diffusions, Stochastics, 20, 247-308 (1987).
    • (1987) Stochastics , vol.20 , pp. 247-308
    • Dawson, D.A.1    Gärtner, J.2
  • 91
    • 0039710560 scopus 로고
    • Quelques exemples familiers en probabilités d’ensembles analytiques non-Boréliens
    • Springer, Berlin
    • DELLACHERIE, C. Quelques exemples familiers en probabilités d’ensembles analytiques non-Boréliens, Séminaire de Probabilités XII: Lecture Notes in Mathematics, Springer, Berlin, 1978, pp. 742-745.
    • (1978) Séminaire de Probabilités XII: Lecture Notes in Mathematics , pp. 742-745
    • Dellacherie, C.1
  • 92
    • 84976126519 scopus 로고
    • Un survoi de la theorie de l’intégrale stochastique
    • DELLACHERIE, C. Un survoi de la theorie de l’intégrale stochastique, Stoch. Proc. Appl., 10, 115-144 (1980).
    • (1980) Stoch. Proc. Appl , vol.10 , pp. 115-144
    • Dellacherie, C.1
  • 94
    • 0004217806 scopus 로고
    • Chaps. I-VI, Hermann, Paris, Chaps. V-VIII, Hermann, Paris, 1980; Chaps. IX-XI, Hermann, Paris, 1983; Chapters XII-XVI (1987)
    • DELLACHERIE, C. and MEYER, P. A. Probabilités et Potentiel, Chaps. I-VI, Hermann, Paris, 1975; Chaps. V-VIII, Hermann, Paris, 1980; Chaps. IX-XI, Hermann, Paris, 1983; Chapters XII-XVI (1987).
    • (1975) Probabilités et Potentiel
    • Dellacherie, C.1    Meyer, P.A.2
  • 95
    • 84860002224 scopus 로고
    • New stochastic methods in physics
    • DE WITT-MORETTE, CECILE and ELWORTHY, K. D. (editors) New stochastic methods in physics, Physics Reports, 77, (3), 121-382 (1981).
    • (1981) Physics Reports , vol.77 , Issue.3 , pp. 121-382
    • De Witt-Morette, C.1    Elworthy, K.D.2
  • 96
    • 0011618394 scopus 로고
    • Existence du processus croissant naturel associé à un potentiel de la classe (D)
    • DOLEANS(-DADE), CATHERINE Existence du processus croissant naturel associé à un potentiel de la classe (D), Z. Wahrscheinlichkeitstheorie, 9, 309-314 (1968).
    • (1968) Z. Wahrscheinlichkeitstheorie , vol.9 , pp. 309-314
    • Doleans, C.1
  • 97
    • 0001125808 scopus 로고
    • Quelques applications de la formule de changement de variables pour les semimartingales
    • DOLEANS(-DADE), CATHERINE Quelques applications de la formule de changement de variables pour les semimartingales, Z. Wahrscheinlichkeitsth., 16, 181-194 (1970).
    • (1970) Z. Wahrscheinlichkeitsth , vol.16 , pp. 181-194
    • Doleans, C.1
  • 100
    • 84931929649 scopus 로고
    • State-spaces for Markov chains
    • DOOB, J. L. State-spaces for Markov chains, Trans. Am. Math. Soc., 149, 279-305 (1970).
    • (1970) Trans. Am. Math. Soc , vol.149 , pp. 279-305
    • Doob, J.L.1
  • 102
    • 0002124082 scopus 로고
    • Liens entre équations différentielles stochastiques et ordinaires
    • DOSS, H. Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. Henri Poincaré B, 13, 99-126 (1977).
    • (1977) Ann. Inst. Henri Poincaré B , vol.13 , pp. 99-126
    • Doss, H.1
  • 107
  • 108
    • 0004188078 scopus 로고
    • English translation in two volumes, Springer, Berlin
    • DYNKIN, E. B. Markov Processes, English translation in two volumes, Springer, Berlin, 1965.
    • (1965) Markov Processes
    • Dynkin, E.B.1
  • 109
    • 0011542337 scopus 로고
    • Non-negative eigenfunctions of the Laplace-Beltrami operator and Brownian motion in certain symmetric spaces (in Russian)
    • DYNKIN, E. B. Non-negative eigenfunctions of the Laplace-Beltrami operator and Brownian motion in certain symmetric spaces (in Russian), Dokl. Akad. Naud SSSR, 141, 288-291 (1961).
    • (1961) Dokl. Akad. Naud SSSR , vol.141 , pp. 288-291
    • Dynkin, E.B.1
  • 110
    • 0001360103 scopus 로고
    • Diffusion of tensors
    • DYNKIN, E. B. Diffusion of tensors, Dokl. Acad. Nauk. SSSR, 179, 1264-1267 (1968).
    • (1968) Dokl. Acad. Nauk. SSSR , vol.179 , pp. 1264-1267
    • Dynkin, E.B.1
  • 112
    • 0011321141 scopus 로고
    • Gaussian and non-Gaussian random fields associated with Markov processes
    • DYNKIN, E. B. Gaussian and non-Gaussian random fields associated with Markov processes, J. Fund. Anal., 55, 344-376 (1984).
    • (1984) J. Fund. Anal , vol.55 , pp. 344-376
    • Dynkin, E.B.1
  • 113
    • 84953276000 scopus 로고    scopus 로고
    • Self-intersection local times, occupation fields and stochastic integrals
    • DYNKIN, E. B. Self-intersection local times, occupation fields and stochastic integrals, (to appear in Advances in Appl. Math.).
    • Advances in Appl. Math
    • Dynkin, E.B.1
  • 116
    • 0003474350 scopus 로고
    • London Mathematical Society Lecture Note Series 20, Cambridge University Press, Cambridge
    • ELWORTHY, K. D. Stochastic Differential Equations on Manifolds, London Mathematical Society Lecture Note Series 20, Cambridge University Press, Cambridge, 1982.
    • (1982) Stochastic Differential Equations on Manifolds
    • Elworthy, K.D.1
  • 119
    • 0011425346 scopus 로고
    • Classical mechanics, the diffusion (heat) equation and the Schrödinger equation on a Riemannian manifold
    • ELWORTHY, K. D. and TRUMAN, A. Classical mechanics, the diffusion (heat) equation and the Schrödinger equation on a Riemannian manifold, J. Math. Phys., 22, (10), 2144-2166 (1981).
    • (1981) J. Math. Phys , vol.22 , Issue.10 , pp. 2144-2166
    • Elworthy, K.D.1    Truman, A.2
  • 120
    • 0040030833 scopus 로고
    • The diffusion equation and classical mechanics: An elementary formula
    • (ed. S. Albeverio et al.), Lecture Notes in Physics, Springer, Berlin
    • ELWORTHY, K. D. and TRUMAN, A. The diffusion equation and classical mechanics: an elementary formula, in Stochastic processes in quantum theory and statistical physics (ed. S. Albeverio et al.), Lecture Notes in Physics, 173, Springer, Berlin, 1982, pp. 136-146.
    • (1982) Stochastic processes in quantum theory and statistical physics , vol.173 , pp. 136-146
    • Elworthy, K.D.1    Truman, A.2
  • 124
    • 0038582982 scopus 로고
    • Boundaries induced by non-negative matrices
    • FELLER, W. Boundaries induced by non-negative matrices, Trans. Am. Math. Soc., 83, 19-54 (1956).
    • (1956) Trans. Am. Math. Soc , vol.83 , pp. 19-54
    • Feller, W.1
  • 125
    • 0347908415 scopus 로고
    • On boundaries and lateral conditions for the Kolmogorov equations
    • Ser. II
    • FELLER, W. On boundaries and lateral conditions for the Kolmogorov equations, Ann. Math., Ser. II, 65, 527-570 (1957).
    • (1957) Ann. Math , vol.65 , pp. 527-570
    • Feller, W.1
  • 126
    • 84972541408 scopus 로고
    • Generalized second-order differential operators and their lateral conditions
    • FELLER, W. Generalized second-order differential operators and their lateral conditions, Illinois J. Math., 1, 459-504 (1957).
    • (1957) Illinois J. Math , vol.1 , pp. 459-504
    • Feller, W.1
  • 132
    • 84972561398 scopus 로고
    • Stochastic differential equations for the non-linear filtering problem
    • FUJISAKI, M., KALLIANPUR, G. and KUNITA, H. Stochastic differential equations for the non-linear filtering problem, Osaka J. Math., 9, 19-40 (1972).
    • (1972) Osaka J. Math , vol.9 , pp. 19-40
    • Fujisaki, M.1    Kallianpur, G.2    Kunita, H.3
  • 134
    • 84972505160 scopus 로고
    • Basic properties of Brownian motion and a capacity on the Wiener space
    • FUKUSHIMA, M. Basic properties of Brownian motion and a capacity on the Wiener space, J. Math. Soc. Japan, 36, 161-176 (1984).
    • (1984) J. Math. Soc. Japan , vol.36 , pp. 161-176
    • Fukushima, M.1
  • 135
    • 0039301626 scopus 로고
    • Une théorie de la dualité à un ensemble polaire près: I
    • GARCIA ALVAREZ, M. A. and MEYER, P. A. Une théorie de la dualité à un ensemble polaire près: I, Ann. Prob., 1, 207-222 (1973).
    • (1973) Ann. Prob , vol.1 , pp. 207-222
    • Garcia Alvarez, M.A.1    Meyer, P.A.2
  • 137
    • 0002902384 scopus 로고
    • Occupation densities
    • GEMAN, D. and HOROWITZ, J. Occupation densities, Ann. Prob., 8, 1-67 (1980).
    • (1980) Ann. Prob , vol.8 , pp. 1-67
    • Geman, D.1    Horowitz, J.2
  • 138
    • 0001854055 scopus 로고
    • A local time analysis of intersections of Brownian paths in the plane
    • GEMAN, D., HOROWITZ, J. and ROSEN, J. A local time analysis of intersections of Brownian paths in the plane, Ann. Prob., 12, 86-107 (1984).
    • (1984) Ann. Prob , vol.12 , pp. 86-107
    • Geman, D.1    Horowitz, J.2    Rosen, J.3
  • 140
    • 0007197086 scopus 로고
    • Excursions of a Markov process
    • GETOOR, R. K. Excursions of a Markov process, Ann. Prob., 8, 244-266 (1979).
    • (1979) Ann. Prob , vol.8 , pp. 244-266
    • Getoor, R.K.1
  • 141
    • 0001799916 scopus 로고
    • Splitting times and shift functionals
    • GETOOR, R. K. Splitting times and shift functionals, Z. Wahrscheinlichkeitstheorie, 47, 69-81 (1979).
    • (1979) Z. Wahrscheinlichkeitstheorie , vol.47 , pp. 69-81
    • Getoor, R.K.1
  • 142
    • 0041510028 scopus 로고
    • Last exit times and additive functionals
    • GETOOR, R. K. and SHARPE, M. J. Last exit times and additive functionals, Ann. Prob., 1, 550-569 (1973).
    • (1973) Ann. Prob , vol.1 , pp. 550-569
    • Getoor, R.K.1    Sharpe, M.J.2
  • 143
    • 0002646610 scopus 로고
    • Excursions of Brownian motion and Bessel process
    • GETOOR, R. K. and SHARPE, M. J. Excursions of Brownian motion and Bessel process, Z. Wahrscheinlichkeitstheorie, 47, 83-106 (1979).
    • (1979) Z. Wahrscheinlichkeitstheorie , vol.47 , pp. 83-106
    • Getoor, R.K.1    Sharpe, M.J.2
  • 144
    • 0042511806 scopus 로고
    • Last exit decompositions and distributions
    • GETOOR, R. K. and SHARPE, M. J. Last exit decompositions and distributions, Indiana Univ. Math. J., 23, 377-404 (1973).
    • (1973) Indiana Univ. Math. J , vol.23 , pp. 377-404
    • Getoor, R.K.1    Sharpe, M.J.2
  • 145
    • 0346034616 scopus 로고
    • Excursions of dual processes
    • GETOOR, R. K. and SHARPE, M. J. Excursions of dual processes, Advances in Math., 45, 259-309 (1982).
    • (1982) Advances in Math , vol.45 , pp. 259-309
    • Getoor, R.K.1    Sharpe, M.J.2
  • 148
    • 0005124162 scopus 로고
    • The mean exit time from a small geodesic ball in a Riemannian manifold
    • GRAY, A. and PINSKY, M. A. The mean exit time from a small geodesic ball in a Riemannian manifold, Bull. Sc. Math., 107, 345-370 (1983).
    • (1983) Bull. Sc. Math , vol.107 , pp. 345-370
    • Gray, A.1    Pinsky, M.A.2
  • 149
    • 0344077365 scopus 로고
    • Construction of local time and Poisson point processes from nested arrays
    • GREENWOOD, P. and PITMAN, J. W. Construction of local time and Poisson point processes from nested arrays, J. London Math. Soc. (2), 22, 182-192 (1980).
    • (1980) J. London Math. Soc , vol.22 , Issue.2 , pp. 182-192
    • Greenwood, P.1    Pitman, J.W.2
  • 150
    • 0001327573 scopus 로고
    • Fluctuation identities for Lévy processes and splitting at the maximum
    • GREENWOOD, P. and PITMAN, J. W. Fluctuation identities for Lévy processes and splitting at the maximum, Adv. Appl. Prob., 12, 893-902 (1980).
    • (1980) Adv. Appl. Prob , vol.12 , pp. 893-902
    • Greenwood, P.1    Pitman, J.W.2
  • 154
    • 0004207439 scopus 로고
    • Van Nostrand, Princeton, NJ
    • HALMOS, P. Measure Theory, Van Nostrand, Princeton, NJ, 1959.
    • (1959) Measure Theory
    • Halmos, P.1
  • 155
    • 0037978348 scopus 로고
    • On the integral representation of Ito processes
    • HAUSSMANN, U. On the integral representation of Ito processes, Stochastics, 3, 17-27 (1979).
    • (1979) Stochastics , vol.3 , pp. 17-27
    • Haussmann, U.1
  • 157
    • 84971176485 scopus 로고
    • Multiple points for symmetric Levy processes
    • HAWKES, J. Multiple points for symmetric Levy processes, Math. Proc. Camb. Phil., 83, 83-90 (1978).
    • (1978) Math. Proc. Camb. Phil , vol.83 , pp. 83-90
    • Hawkes, J.1
  • 158
    • 84916531149 scopus 로고
    • The measure of the range of a subordinator
    • HAWKES, J. The measure of the range of a subordinator, Bull. London Math. Soc., 5, 21-28 (1973).
    • (1973) Bull. London Math. Soc , vol.5 , pp. 21-28
    • Hawkes, J.1
  • 161
    • 84935021209 scopus 로고
    • American Mathematical Society Colloquium Publications, Providence, RI
    • HILLE, E. and PHILLIPS, R. S. Functional Analysis and Semigroups, American Mathematical Society Colloquium Publications, Providence, RI, 1957.
    • (1957) Functional Analysis and Semigroups
    • Hille, E.1    Phillips, R.S.2
  • 162
    • 84953285273 scopus 로고
    • Applications of dual processes to diffusion theory
    • Urbana
    • HOLLEY, R., STROOCK, D. W. and WILLIAMS, D. Applications of dual processes to diffusion theory, Proc. AMS Prob. Symp., Urbana, 1976, pp. 23-36.
    • (1976) Proc. AMS Prob. Symp , pp. 23-36
    • Holley, R.1    Stroock, D.W.2    Williams, D.3
  • 163
    • 15244346736 scopus 로고
    • Hypoelliptic second-order differential equations
    • HORMANDER, L. Hypoelliptic second-order differential equations, Acta Math., 117, 147-171 (1967).
    • (1967) Acta Math , vol.117 , pp. 147-171
    • Hormander, L.1
  • 164
    • 0013481375 scopus 로고
    • On excursions of reflecting Brownian motion
    • HSU, P. On excursions of reflecting Brownian motion, Trans. Amer. Math. Soc., 296, 239-264 (1986).
    • (1986) Trans. Amer. Math. Soc , vol.296 , pp. 239-264
    • Hsu, P.1
  • 166
    • 84972528343 scopus 로고
    • Markoff processes and potentials: I, II, III
    • 2, 151-213 (1958)
    • HUNT, G. A. Markoff processes and potentials: I, II, III, Illinois J. Math., 1,44-93; 316-369 (1957); 2, 151-213 (1958).
    • (1957) Illinois J. Math , vol.1
    • Hunt, G.A.1
  • 169
    • 0001455484 scopus 로고
    • Stochastic integral
    • ITÔ, K. Stochastic integral, Proc. Imp. Acad. Tokyo, 20, 519-524 (1944).
    • (1944) Proc. Imp. Acad. Tokyo , vol.20 , pp. 519-524
    • Itô, K.1
  • 170
    • 0039769080 scopus 로고
    • On a stochastic integral equation
    • ITÔ, K. On a stochastic integral equation, Proc. Imp. Acad. Tokyo, 22, 32-35 (1946).
    • (1946) Proc. Imp. Acad. Tokyo , vol.22 , pp. 32-35
    • Itô, K.1
  • 171
    • 84867562332 scopus 로고
    • Stochastic differential equations in a differential manifold
    • ITÔ, K. Stochastic differential equations in a differential manifold, Nagoya Math. J., 1, 35-47 (1950).
    • (1950) Nagoya Math. J , vol.1 , pp. 35-47
    • Itô, K.1
  • 172
    • 0002770070 scopus 로고
    • The Brownian motion and tensor fields on a Riemannian manifold
    • ITÔ, K. The Brownian motion and tensor fields on a Riemannian manifold, Proc. Intern. Congr. Math., Stockholm, 1963, pp. 536-539.
    • (1963) Proc. Intern. Congr. Math., Stockholm , pp. 536-539
    • Itô, K.1
  • 174
    • 0001050284 scopus 로고
    • Poisson point processes attached to Markov processes
    • Vol. 3, University of California Press
    • ITÔ, K. Poisson point processes attached to Markov processes, Proc. 6th Berkeley Symp. Math. Statist. Prob., Vol. 3, University of California Press, 1971, pp. 225-240.
    • (1971) Proc. 6th Berkeley Symp. Math. Statist. Prob , pp. 225-240
    • Itô, K.1
  • 177
    • 0020880259 scopus 로고
    • A finite fuel stochastic control problem
    • JACKA, S. A finite fuel stochastic control problem, Stochastics, 10, 103-113 (1983).
    • (1983) Stochastics , vol.10 , pp. 103-113
    • Jacka, S.1
  • 179
    • 0013309131 scopus 로고
    • Splitting times for Markov processes and a generalised Markov property for diffusions
    • JACOBSEN, M. Splitting times for Markov processes and a generalised Markov property for diffusions, Z. IVahrscheinlichkeitstheorie, 30, 27-43 (1974).
    • (1974) Z. IVahrscheinlichkeitstheorie , vol.30 , pp. 27-43
    • Jacobsen, M.1
  • 181
    • 0001894033 scopus 로고
    • A general theorem of representation for martingales
    • JACOD, J. A general theorem of representation for martingales, Proc. AMS Prob. Symp., Urbana, 1976, pp. 37-53.
    • (1976) Proc. AMS Prob. Symp., Urbana , pp. 37-53
    • Jacod, J.1
  • 183
    • 0041069920 scopus 로고
    • Etude des solutions extrémales et représentation intégrale des solutions pour certains problèmes de martingales
    • JACOD, J. and YOR, M. Etude des solutions extrémales et représentation intégrale des solutions pour certains problèmes de martingales, Z. Wahrscheinlichkeitsth., 38, 83-125 (1977).
    • (1977) Z. Wahrscheinlichkeitsth , vol.38 , pp. 83-125
    • Jacod, J.1    Yor, M.2
  • 188
    • 84939007907 scopus 로고
    • An innovations approach to least squares estimation, Part I: Linear filtering with additive white noise
    • KAILATH, T. An innovations approach to least squares estimation, Part I: Linear filtering with additive white noise, IEEE Trans. Automatic Control, 13, 646-655 (1968).
    • (1968) IEEE Trans. Automatic Control , vol.13 , pp. 646-655
    • Kailath, T.1
  • 190
    • 0001753639 scopus 로고
    • Pole-seeking Brownian motion and bird navigation (with discussion)
    • KENDALL, D. G. Pole-seeking Brownian motion and bird navigation (with discussion), J. Roy. Statist. Soc. B, 36, 365-417 (1974).
    • (1974) J. Roy. Statist. Soc , vol.36 B , pp. 365-417
    • Kendall, D.G.1
  • 191
    • 0000291561 scopus 로고
    • The diffusion of shape
    • KENDALL, D. G. The diffusion of shape, Adv. Appl. Prob., 9, 428-430 (1979).
    • (1979) Adv. Appl. Prob , vol.9 , pp. 428-430
    • Kendall, D.G.1
  • 192
    • 0002432238 scopus 로고
    • Shape manifolds, Procrustean metrics, and complex projective spaces
    • KENDALL, D. G. Shape manifolds, Procrustean metrics, and complex projective spaces, Bull. London Math. Soc., 16, 81-121 (1984).
    • (1984) Bull. London Math. Soc , vol.16 , pp. 81-121
    • Kendall, D.G.1
  • 193
    • 77957180480 scopus 로고
    • A totally unstable Markov process
    • KENDALL, D. G. A totally unstable Markov process, Quarterly J. Math. Oxford, 9, (34), 149-160(1958).
    • (1958) Quarterly J. Math. Oxford , vol.9 , Issue.34 , pp. 149-160
    • Kendall, D.G.1
  • 194
    • 84953320190 scopus 로고
    • (special supplement to Adv. Appl. Prob. to honour G. E. H. Reuter), Applied Prob. Trust
    • KENDALL, D. G. (Editor) Analytic and geometric stochastics (special supplement to Adv. Appl. Prob. to honour G. E. H. Reuter), Applied Prob. Trust, 1986.
    • (1986) Analytic and geometric stochastics
    • Kendall, D.G.1
  • 195
    • 0007077043 scopus 로고
    • Some pathological Markov processes with a denumerable infinity of states and the associated contraction semigroups of operators on I
    • 377-115, 1954 (Amsterdam)
    • KENDALL, D. G. and REUTER, G. E. H. Some pathological Markov processes with a denumerable infinity of states and the associated contraction semigroups of operators on I, Proc. Intern. Congress Math. 1954 (Amsterdam), 3, 377-115 (1956).
    • (1956) Proc. Intern. Congress Math , vol.3
    • Kendall, D.G.1    Reuter, G.E.H.2
  • 196
    • 67650236078 scopus 로고
    • Knotting of Brownian motion in 3-space
    • KENDALL, W. S. Knotting of Brownian motion in 3-space, J. London Math. Soc. (2), 19,378-384 (1979).
    • (1979) J. London Math. Soc , vol.19 , Issue.2 , pp. 378-384
    • Kendall, W.S.1
  • 200
    • 0001251792 scopus 로고
    • Some probabilistic properties of Bessel functions
    • KENT, J. Some probabilistic properties of Bessel functions, Ann. Prob., 6, 760-770 (1978).
    • (1978) Ann. Prob , vol.6 , pp. 760-770
    • Kent, J.1
  • 201
    • 0346405945 scopus 로고
    • The infinite divisibility of the von Mises-Fisher distribution for all values of the parameter in all dimensions
    • KENT, J. The infinite divisibility of the von Mises-Fisher distribution for all values of the parameter in all dimensions. Proc. London Math. Soc., 3, (35), 359-384 (1977).
    • (1977) Proc. London Math. Soc , vol.3 , Issue.35 , pp. 359-384
    • Kent, J.1
  • 202
    • 0000073325 scopus 로고
    • Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations
    • KHASMINSKII, R. Z. Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations, Th. Prob. and Appl., 5, 179-196 (1960).
    • (1960) Th. Prob. and Appl , vol.5 , pp. 179-196
    • Khasminskii, R.Z.1
  • 205
    • 0001159401 scopus 로고
    • Subadditive ergodic theory
    • KINGMAN, J. F. C. Subadditive ergodic theory, Ann. Prob., 1, 883-909 (1973).
    • (1973) Ann. Prob , vol.1 , pp. 883-909
    • Kingman, J.F.C.1
  • 206
    • 84969653882 scopus 로고
    • Completely random measures
    • KINGMAN, J. F. C. Completely random measures, Pacific J. Math., 21, 59-78 (1967).
    • (1967) Pacific J. Math , vol.21 , pp. 59-78
    • Kingman, J.F.C.1
  • 208
    • 84972521598 scopus 로고
    • Note on régularisation of Markov processes
    • KNIGHT, F. B. Note on régularisation of Markov processes, Illinois J. Math., 9, 548-552 (1965).
    • (1965) Illinois J. Math , vol.9 , pp. 548-552
    • Knight, F.B.1
  • 210
    • 84968484961 scopus 로고
    • Random walks and the sojourn density process of Brownian motion
    • KNIGHT, F. B. Random walks and the sojourn density process of Brownian motion, Trans. Amer. Math. Soc., 107, 56-86 (1963).
    • (1963) Trans. Amer. Math. Soc , vol.107 , pp. 56-86
    • Knight, F.B.1
  • 213
    • 0001479882 scopus 로고
    • Necessary and sufficient conditions for almost sure sample stability of linear Itô equations
    • KOZIN, F. and PRODROMOU, S. Necessary and sufficient conditions for almost sure sample stability of linear Itô equations, SIAM J. Appl. Math., 21, 413-425 (1971).
    • (1971) SIAM J. Appl. Math , vol.21 , pp. 413-425
    • Kozin, F.1    Prodromou, S.2
  • 215
    • 84953252774 scopus 로고
    • The law of the iterated logarithm for Banach space valued random variables
    • Springer, Berlin
    • KUELBS, J. The law of the iterated logarithm for Banach space valued random variables, in Probability in Banach Spaces: Lecture Notes in Mathematics 526, Springer, Berlin, 1976, pp. 131-142.
    • (1976) Probability in Banach Spaces: Lecture Notes in Mathematics 526 , pp. 131-142
    • Kuelbs, J.1
  • 216
    • 0000606190 scopus 로고
    • On the decomposition of the solutions of stochastic differential equations
    • Springer, Berlin
    • KUNITA, H. On the decomposition of the solutions of stochastic differential equations, in Stochastic Integrals: Lecture Notes in Mathematics 851, Springer, Berlin, 1981, pp. 213-255.
    • (1981) Stochastic Integrals: Lecture Notes in Mathematics 851 , pp. 213-255
    • Kunita, H.1
  • 217
    • 0020005664 scopus 로고
    • On backward stochastic differential equations
    • KUNITA, H. On backward stochastic differential equations, Stochastics, 6, 293-313 (1982).
    • (1982) Stochastics , vol.6 , pp. 293-313
    • Kunita, H.1
  • 220
    • 84972538901 scopus 로고
    • On square integrable martingales
    • KUNITA, H. and WATANABE, S. On square integrable martingales, Nagoya Math. J., 30, 209-245 (1967).
    • (1967) Nagoya Math. J , vol.30 , pp. 209-245
    • Kunita, H.1    Watanabe, S.2
  • 221
    • 3042851422 scopus 로고
    • Some theorems concerning resolvents over locally compact spaces
    • Vol. 2, Part 2, University of California Press
    • KUNITA, H. and WATANABE, T. Some theorems concerning resolvents over locally compact spaces, in Proc. 5th Berkeley Symp. Math. Statist. Prob., Vol. 2, Part 2, University of California Press, 1967, pp. 131-164.
    • (1967) Proc. 5th Berkeley Symp. Math. Statist. Prob , pp. 131-164
    • Kunita, H.1    Watanabe, T.2
  • 222
    • 84972514341 scopus 로고
    • Markov processes and Martin boundaries, I
    • KUNITA, H. and WATANABE, T. Markov processes and Martin boundaries, I, Illinois J. Math., 9, 485-526 (1965).
    • (1965) Illinois J. Math , vol.9 , pp. 485-526
    • Kunita, H.1    Watanabe, T.2
  • 223
    • 0043196004 scopus 로고
    • On certain reversed processes and their application to potential theory and boundary theory
    • KUNITA, H. and WATANABE, T. On certain reversed processes and their application to potential theory and boundary theory, J. Math. Mech., 15, 393-434 (1966).
    • (1966) J. Math. Mech , vol.15 , pp. 393-434
    • Kunita, H.1    Watanabe, T.2
  • 225
    • 0002556345 scopus 로고
    • Applications of the Malliavin calculus, Part II
    • KUSUOKA, S. and STROOCK, D. Applications of the Malliavin calculus, Part II, J. Fac. Sci. U. of Tokyo (IA), 32,1-76 (1985).
    • (1985) J. Fac. Sci. U. of Tokyo , vol.32 IA , pp. 1-76
    • Kusuoka, S.1    Stroock, D.2
  • 226
    • 0005408815 scopus 로고
    • Applications du temps local aux equations différentielles stochastiques unidimension- elles
    • Springer, Berlin
    • LE GALL, J.-F. Applications du temps local aux equations différentielles stochastiques unidimension- elles, Séminaire de Probabilités X VII: Lecture Notes in Mathematics 986, Springer, Berlin, 1983, pp. 15-31.
    • (1983) Séminaire de Probabilités X VII: Lecture Notes in Mathematics 986 , pp. 15-31
    • Le Gall, J.-F.1
  • 227
    • 0000011756 scopus 로고
    • Sur la saucisse de Wiener et les points multiples du mouvement Brownien
    • LE GALL, J.-F. Sur la saucisse de Wiener et les points multiples du mouvement Brownien, Ann. Prob., 14, 1219-1244 (1986).
    • (1986) Ann. Prob , vol.14 , pp. 1219-1244
    • Le Gall, J.-F.1
  • 228
    • 0000389346 scopus 로고
    • Sur les temps local d’intersection du mouvement Brownien plan et la méthode de renormalization de Varadhan
    • Springer, Berlin
    • LE GALL, J.-F. Sur les temps local d’intersection du mouvement Brownien plan et la méthode de renormalization de Varadhan, Séminaire de Probabilités XIX: Lecture Notes in Mathematics 1123, Springer, Berlin, 1985, pp. 314-331.
    • (1985) Séminaire de Probabilités XIX: Lecture Notes in Mathematics 1123 , pp. 314-331
    • Le Gall, J.-F.1
  • 232
    • 0040539257 scopus 로고
    • Systèmes markoviens et stationnaires. Cas dénombrable
    • 69, 203-212 (1952)
    • LEVY, P. Systèmes markoviens et stationnaires. Cas dénombrable, Ann. Ecole Norm. Sup. (3), 68, 327-381 (1951); 69, 203-212 (1952).
    • (1951) Ann. Ecole Norm. Sup , vol.68 , Issue.3 , pp. 327-381
    • Levy, P.1
  • 233
    • 84953247299 scopus 로고
    • Processus markoviens et stationnaires due cinquième type (infinité dénombrable des états possibles, paramétré continu)
    • LEVY, P. Processus markoviens et stationnaires due cinquième type (infinité dénombrable des états possibles, paramétré continu). C. R. Acad. Sci. Paris, 236, 1630-1632 (1953).
    • (1953) C. R. Acad. Sci. Paris , vol.236 , pp. 1630-1632
    • Levy, P.1
  • 234
    • 4243423870 scopus 로고
    • Processus markoviens et stationnaires. Cas dénombrable
    • LEVY, P. Processus markoviens et stationnaires. Cas dénombrable. Ann. Inst H. Poincaré, 16, 7-25 (1958).
    • (1958) Ann. Inst H. Poincaré , vol.16 , pp. 7-25
    • Levy, P.1
  • 235
    • 0042511829 scopus 로고
    • Brownian motion on a submanifold of Euclidean space
    • LEWIS, J. T. Brownian motion on a submanifold of Euclidean space, Bull. London Math. Soc., 18, 616-20 (1986).
    • (1986) Bull. London Math. Soc , vol.18 , pp. 616-620
    • Lewis, J.T.1
  • 237
    • 0020721241 scopus 로고
    • On coupling of diffusion processes
    • LINDVALL, T. On coupling of diffusion processes, J. Appl. Probab., 20, 82-93 (1983).
    • (1983) J. Appl. Probab , vol.20 , pp. 82-93
    • Lindvall, T.1
  • 240
    • 33747029430 scopus 로고
    • Finely holomorphic functions
    • LYONS, T. J. Finely holomorphic functions, J. Funct. Anal., 37, 1-18 (1980).
    • (1980) J. Funct. Anal , vol.37 , pp. 1-18
    • Lyons, T.J.1
  • 243
    • 0001561109 scopus 로고
    • Windings of the plane Brownian motion
    • LYONS, T. J. and MCKEAN, H. P. Windings of the plane Brownian motion. Adv. Math., 51, 212-225 (1984).
    • (1984) Adv. Math , vol.51 , pp. 212-225
    • Lyons, T.J.1    McKean, H.P.2
  • 244
    • 33745695719 scopus 로고
    • Systèmes régéneratifs
    • Société Mathématique de France
    • MAISONNEUVE, B. Systèmes régéneratifs, Asterique, 15, Société Mathématique de France, 1974.
    • (1974) Asterique , vol.15
    • Maisonneuve, B.1
  • 246
    • 0002684408 scopus 로고
    • Stochastic calculus of variation and hypo-elliptic operators
    • Kyoto, (ed. K. Itô), Kinokuniya-Wiley, 1978
    • MALLIAVIN, P. Stochastic calculus of variation and hypo-elliptic operators, Proc. Intern. Symp. Stock. Diff. Equations, Kyoto, 1976 (ed. K. Itô), Kinokuniya-Wiley, 1978, pp, 195-263.
    • (1976) Proc. Intern. Symp. Stock. Diff. Equations , pp. 195-263
    • Malliavin, P.1
  • 247
    • 0001694213 scopus 로고
    • k-hypoellipticity with degeneracy
    • (ed. A. Friedman and M. Pinsky), Academic Press, New York
    • k-hypoellipticity with degeneracy, in Stochastic Analysis (ed. A. Friedman and M. Pinsky), Academic Press, New York, 1978, pp. 199-214.
    • (1978) Stochastic Analysis , pp. 199-214
    • Malliavin, P.1
  • 248
    • 49549151946 scopus 로고
    • Formule de la moyenne, calcul de perturbations et théorèmes d’annulation pour les formes harmoniques
    • MALLIAVIN, P. Formule de la moyenne, calcul de perturbations et théorèmes d’annulation pour les formes harmoniques, J. Funct. Anal., 17, 274-291 (1974).
    • (1974) J. Funct. Anal , vol.17 , pp. 274-291
    • Malliavin, P.1
  • 249
    • 0000824004 scopus 로고
    • Factorisations et lois limites de la diffusion horizontale au dessus d’un espace riemmanien symmetrique
    • Springer, Berlin
    • MALLIAVIN, M. P. and MALLIAVIN, P. Factorisations et lois limites de la diffusion horizontale au dessus d’un espace riemmanien symmetrique, Lecture Notes in Mathematics 404, Springer, Berlin, 1974, pp. 166-217.
    • (1974) Lecture Notes in Mathematics 404 , pp. 166-217
    • Malliavin, M.P.1    Malliavin, P.2
  • 250
    • 0000786340 scopus 로고
    • Minimal positive harmonie functions
    • MARTIN, R. S. Minimal positive harmonie functions, Trans. Am. Math. Soc., 49, 137-164 (1941).
    • (1941) Trans. Am. Math. Soc , vol.49 , pp. 137-164
    • Martin, R.S.1
  • 251
    • 34250225848 scopus 로고
    • Calculation of some conditional excursion formulae
    • MCGILL, P. Calculation of some conditional excursion formulae, Z. Wahrscheinlichkeitstheorie, 61, 255-260 (1982).
    • (1982) Z. Wahrscheinlichkeitstheorie , vol.61 , pp. 255-260
    • McGill, P.1
  • 252
    • 0038866985 scopus 로고
    • Markov properties of diffusion local time: A martingale approach
    • MCGILL, P. Markov properties of diffusion local time: a martingale approach, Adv. Appl. Prob., 14, 789-810 (1980).
    • (1980) Adv. Appl. Prob , vol.14 , pp. 789-810
    • McGill, P.1
  • 253
    • 0141607462 scopus 로고
    • Integral representation of martingales in the Brownian excursion filtration
    • Springer, Berlin
    • MCGILL, P. Integral representation of martingales in the Brownian excursion filtration, Séminaire de Probabilités XX: Lecture Notes in Mathematics 1204, Springer, Berlin, 1986, pp. 465-502.
    • (1986) Séminaire de Probabilités XX: Lecture Notes in Mathematics 1204 , pp. 465-502
    • McGill, P.1
  • 255
    • 0011003356 scopus 로고
    • Excursions of a non-singular diffusion
    • MCKEAN, H. P. Excursions of a non-singular diffusion, Z. Wahrscheinlichkeitstheorie, 1, 230-239 (1963).
    • (1963) Z. Wahrscheinlichkeitstheorie , vol.1 , pp. 230-239
    • McKean, H.P.1
  • 256
    • 0011416762 scopus 로고
    • Brownian local times
    • MCKEAN, H. P. Brownian local times, Adv. Math., 16, 91-111 (1975).
    • (1975) Adv. Math , vol.16 , pp. 91-111
    • McKean, H.P.1
  • 257
    • 84878943962 scopus 로고
    • A regularity condition on the transition probability measure of a diffusion process
    • MCNAMARA, J. M. A regularity condition on the transition probability measure of a diffusion process. Stochastics, 15, 161-182 (1985).
    • (1985) Stochastics , vol.15 , pp. 161-182
    • McNamara, J.M.1
  • 259
    • 4243882935 scopus 로고
    • Application du calcul stochastique à l’étude de processus de Markov réguliers sur [0,1]
    • MELÉARD, S. Application du calcul stochastique à l’étude de processus de Markov réguliers sur [0,1], Stochastics, 19, 41-82 (1986).
    • (1986) Stochastics , vol.19 , pp. 41-82
    • Meléard, S.1
  • 262
    • 0003952910 scopus 로고
    • (English translation), Blaisdell, Waltham, Mass
    • MEYER, P. A. Probability and Potential (English translation), Blaisdell, Waltham, Mass., 1966.
    • (1966) Probability and Potential
    • Meyer, P.A.1
  • 266
    • 0013380799 scopus 로고
    • Démonstration probabiliste de certaines inégalités de Littlewood-Paley
    • Springer, Berlin
    • MEYER, P. A. Démonstration probabiliste de certaines inégalités de Littlewood-Paley, Sèm. de Probabilités X: Lecture Notes in Mathematics 511, Springer, Berlin, 1976, pp. 125-183.
    • (1976) Sèm. de Probabilités X: Lecture Notes in Mathematics 511 , pp. 125-183
    • Meyer, P.A.1
  • 268
  • 272
    • 0000532550 scopus 로고
    • Approximate integration of stochastic differential equations
    • MIHLSTEIN, G. N. Approximate integration of stochastic differential equations, Th. Prob. Appl, 19, 557-562 (1974).
    • (1974) Th. Prob. Appl , vol.19 , pp. 557-562
    • Mihlstein, G.N.1
  • 273
    • 33747348631 scopus 로고
    • Random times and decomposition theorems
    • American Mathematical Society, Providence, RI
    • MILLAR, P. W. Random times and decomposition theorems, in Probability: Proc. Symp. Pure Math. XXXI, American Mathematical Society, Providence, RI, 1977, pp. 91-103.
    • (1977) Probability: Proc. Symp. Pure Math. XXXI , pp. 91-103
    • Millar, P.W.1
  • 274
    • 0001680696 scopus 로고
    • A path decomposition for Markov processes
    • MILLAR, P. W. A path decomposition for Markov processes, Ann. Prob., 6, 345-348 (1978).
    • (1978) Ann. Prob , vol.6 , pp. 345-348
    • Millar, P.W.1
  • 276
    • 84896997602 scopus 로고    scopus 로고
    • Non-linear filtering and stochastic control
    • Springer, Berlin
    • MITTER, S. K. and MORO, A. (editors) Non-linear filtering and stochastic control, Lecture Notes in Mathematics 972, Springer, Berlin, 1982.
    • (1982) Lecture Notes in Mathematics 972
    • Mitter, S.K.1    Moro, A.2
  • 277
    • 84884000868 scopus 로고
    • Application of additive functionals to the boundary problem of Markov processes (Lèvy’s system of U-processes)
    • Univ. Calif. Press, Berkeley
    • MOTOO, M. Application of additive functionals to the boundary problem of Markov processes (Lèvy’s system of U-processes), Proc. Fifth Berkeley Symposium Math. Statist. Prob. 11(2), Univ. Calif. Press, Berkeley, 1967, pp. 75-110.
    • (1967) Proc. Fifth Berkeley Symposium Math. Statist. Prob , vol.11 , Issue.2 , pp. 75-110
    • Motoo, M.1
  • 278
    • 34047177003 scopus 로고
    • On a class of additive functionals of Markov processes
    • MOTOO, M. and WATANABE, S. On a class of additive functionals of Markov processes, J. Math. Kyoto Univ., 4, 429-469 (1965).
    • (1965) J. Math. Kyoto Univ , vol.4 , pp. 429-469
    • Motoo, M.1    Watanabe, S.2
  • 279
    • 84972574822 scopus 로고
    • On the path wise uniqueness of solutions of one-dimensional stochastic differential equations
    • NAKAO, S. On the path wise uniqueness of solutions of one-dimensional stochastic differential equations, Osaka J. Math., 9, 513-518 (1972).
    • (1972) Osaka J. Math , vol.9 , pp. 513-518
    • Nakao, S.1
  • 280
    • 0002702476 scopus 로고
    • The imbedding problem for Riemannian manifolds
    • NASH, J. F. The imbedding problem for Riemannian manifolds, Ann. of Math., 63,20-63 (1956).
    • (1956) Ann. of Math , vol.63 , pp. 20-63
    • Nash, J.F.1
  • 284
    • 84932259883 scopus 로고
    • Sur les états d’entrée et les états fictifs d’un processus de Markov
    • NEVEU, J. Sur les états d’entrée et les états fictifs d’un processus de Markov, Ann. Inst. Henri Poincaré, 17, 323-337 (1962).
    • (1962) Ann. Inst. Henri Poincaré , vol.17 , pp. 323-337
    • Neveu, J.1
  • 285
    • 84932562346 scopus 로고
    • Lattice methods and submarkovian processes
    • Vol. 2, University of California Press
    • NEVEU, J. Lattice methods and submarkovian processes, Proc. 4th Berkeley Symp. Math. Statist. Prob., Vol. 2, University of California Press, 1960, pp. 347-391.
    • (1960) Proc. 4th Berkeley Symp. Math. Statist. Prob , pp. 347-391
    • Neveu, J.1
  • 286
    • 0141546965 scopus 로고
    • Une généralisation des processus à accroissements positifs indépendants
    • NEVEU, J. Une généralisation des processus à accroissements positifs indépendants, Abh. Math. Sem. Univ. Hamburg, 25, 36-61 (1961).
    • (1961) Abh. Math. Sem. Univ. Hamburg , vol.25 , pp. 36-61
    • Neveu, J.1
  • 287
    • 84951559549 scopus 로고
    • Entrance, exit and fictitious states for Markov chains
    • NEVEU, J. Entrance, exit and fictitious states for Markov chains, Proc. Aarhus Colloq. Combin. Prob., 1962, pp. 64-68.
    • (1962) Proc. Aarhus Colloq. Combin. Prob , pp. 64-68
    • Neveu, J.1
  • 290
    • 0000904596 scopus 로고
    • Self-avoiding random walk: A Brownian motion model with local time drift
    • NORRIS, J. R., ROGERS, L. C. G. and WILLIAMS, D. Self-avoiding random walk: a Brownian motion model with local time drift, Prob. Thy. and Rel. Fields, 74, 271-287 (1987).
    • (1987) Prob. Thy. and Rel. Fields , vol.74 , pp. 271-287
    • Norris, J.R.1    Rogers, L.C.G.2    Williams, D.3
  • 291
    • 0021443346 scopus 로고
    • Malliavin’s calculus and stochastic integral: Representation of functionals of diffusion processes
    • OCONE, D. Malliavin’s calculus and stochastic integral: representation of functionals of diffusion processes, Stochastics, 12, 161-185 (1984).
    • (1984) Stochastics , vol.12 , pp. 161-185
    • Ocone, D.1
  • 293
    • 0018768309 scopus 로고
    • Stochastic differential equations and filtering of diffusion processes
    • PARDOUX, E. Stochastic differential equations and filtering of diffusion processes, Stochastics, 3, 127-167 (1979).
    • (1979) Stochastics , vol.3 , pp. 127-167
    • Pardoux, E.1
  • 294
    • 0001885676 scopus 로고
    • Grossissement d’une filtration et retournement du temps d’une diffusion
    • Springer, Berlin
    • ORIHARA, A. Grossissement d’une filtration et retournement du temps d’une diffusion, Sëm. de Probabilités XX: Lecture Notes in Mathematics 1204, Springer, Berlin, 1986, pp. 48-55.
    • (1986) Sëm. de Probabilités XX: Lecture Notes in Mathematics 1204 , pp. 48-55
    • Orihara, A.1
  • 296
    • 84953232411 scopus 로고    scopus 로고
    • Discretization and simulation of stochastic differential equations
    • PARDOUX, E. and TALAY, D. Discretization and simulation of stochastic differential equations, to appear in Acta Appl. Math.
    • Acta Appl. Math
    • Pardoux, E.1    Talay, D.2
  • 298
    • 84953339579 scopus 로고    scopus 로고
    • Paper on Brownian motions on homogeneous spaces, to appear
    • PAUWELS, E. and ROGERS, L. C. G. Paper on Brownian motions on homogeneous spaces (to appear).
    • Pauwels, E.1    Rogers, L.C.G.2
  • 299
    • 0005498596 scopus 로고
    • Local time and path wise uniqueness for stochastic differential equations
    • Springer, Berlin
    • PERKINS, E. Local time and path wise uniqueness for stochastic differential equations, Sent, de Probabilités XVI: Lecture Notes in Mathematics 920, Springer, Berlin, 1982, pp. 201-208.
    • (1982) Sent, de Probabilités XVI: Lecture Notes in Mathematics 920 , pp. 201-208
    • Perkins, E.1
  • 300
    • 0009234368 scopus 로고
    • Local time is a semimartingale
    • PERKINS, E. Local time is a semimartingale, Z. Wahrscheinlichtkeitsth., 60, 79-117 (1982).
    • (1982) Z. Wahrscheinlichtkeitsth , vol.60 , pp. 79-117
    • Perkins, E.1
  • 303
    • 0038609746 scopus 로고
    • Stochastic Riemannian geometry
    • ed. A. T. Bharucha-Reid, Academic Press, New York
    • PINSKY, M. A. Stochastic Riemannian geometry, in Probabilistic Analysis and Related Topics, 1 (ed. A. T. Bharucha-Reid), Academic Press, New York, 1978.
    • (1978) Probabilistic Analysis and Related Topics , vol.1
    • Pinsky, M.A.1
  • 304
    • 0000884985 scopus 로고
    • One-dimensional Brownian motion and the three-dimensional Bessel process
    • PITMAN, J. W. One-dimensional Brownian motion and the three-dimensional Bessel process, J. Appl. Prob., 7, 511-526 (1975).
    • (1975) J. Appl. Prob , vol.7 , pp. 511-526
    • Pitman, J.W.1
  • 305
    • 84953329122 scopus 로고
    • Path decomposition for conditional Brownian motion
    • Preprint № 11
    • PITMAN, J. W. Path decomposition for conditional Brownian motion, Inst. Math. Statist. Univ. Copenhagen, Preprint № 11 (1974).
    • (1974) Inst. Math. Statist. Univ. Copenhagen
    • Pitman, J.W.1
  • 308
    • 0000674721 scopus 로고
    • A decomposition of Bessel bridges
    • PITMAN, J. W. and YOR, M. A decomposition of Bessel bridges. Z. Wahrscheinlichkeitsth., 59, 425-457 (1982).
    • (1982) Z. Wahrscheinlichkeitsth , vol.59 , pp. 425-457
    • Pitman, J.W.1    Yor, M.2
  • 309
    • 84968494876 scopus 로고
    • The asymptotic joint distribution of windings of planar Brownian motion
    • PITMAN, J. W. and YOR, M. The asymptotic joint distribution of windings of planar Brownian motion, Bull. Amer. Math. Soc., 10, 109-111 (1984).
    • (1984) Bull. Amer. Math. Soc , vol.10 , pp. 109-111
    • Pitman, J.W.1    Yor, M.2
  • 310
    • 0000030777 scopus 로고
    • Asymptotic laws of planar Brownian motion
    • PITMAN, J. W. and YOR, M. Asymptotic laws of planar Brownian motion, Ann. Probab., 14, 733-779 (1986).
    • (1986) Ann. Probab , vol.14 , pp. 733-779
    • Pitman, J.W.1    Yor, M.2
  • 311
    • 84968486053 scopus 로고
    • Coterminal families and the strong Markov property
    • PITTENGER, A. O. and SHIH, C. T. Coterminal families and the strong Markov property, Trans. Amer. Math. Soc., 182, 1-42 (1973).
    • (1973) Trans. Amer. Math. Soc , vol.182 , pp. 1-42
    • Pittenger, A.O.1    Shih, C.T.2
  • 313
    • 84953211838 scopus 로고
    • Classical potential theory and Brownian motion
    • Vol. 3, University of California Press
    • PORT, S. C. and STONE, C. J. Classical potential theory and Brownian motion, Proc. 6th Berkeley Symp. Math. Statist. Prob., Vol. 3, University of California Press, 1972, pp. 143-176.
    • (1972) Proc. 6th Berkeley Symp. Math. Statist. Prob , pp. 143-176
    • Port, S.C.1    Stone, C.J.2
  • 314
    • 84953330366 scopus 로고
    • Logarithmic potentials and planar Brownian motion
    • Vol. 3, University of California Press
    • PORT, S. C. and STONE, C. J. Logarithmic potentials and planar Brownian motion, Proc. 6th Berkeley Symp. Math. Statist. Prob., Vol. 3, University of California Press, 1972, pp. 177-192.
    • (1972) Proc. 6th Berkeley Symp. Math. Statist. Prob , pp. 177-192
    • Port, S.C.1    Stone, C.J.2
  • 317
    • 0000033355 scopus 로고
    • Convergence of random processes and limit theorems in probability
    • PROHOROV, YU. V. Convergence of random processes and limit theorems in probability, Theor. Prob. Applic., 1, 157-214 (1956).
    • (1956) Theor. Prob. Applic , vol.1 , pp. 157-214
    • Prohorov, Y.V.1
  • 318
    • 0001346915 scopus 로고
    • On the existence, uniqueness, convergence and explosions of solutions of stochastic differential equations
    • PROTTER, P. On the existence, uniqueness, convergence and explosions of solutions of stochastic differential equations, Ann. Probab., 5, 243-261 (1977).
    • (1977) Ann. Probab , vol.5 , pp. 243-261
    • Protter, P.1
  • 319
    • 0011668080 scopus 로고
    • On decomposition theorems of Meyer
    • RAO, K. M. On decomposition theorems of Meyer, Math. Scand., 24, 66-78 (1969).
    • (1969) Math. Scand , vol.24 , pp. 66-78
    • Rao, K.M.1
  • 320
    • 0039273652 scopus 로고
    • Quasimartingales
    • RAO, K. M. Quasimartingales, Math. Scand., 24, 79-92 (1969).
    • (1969) Math. Scand , vol.24 , pp. 79-92
    • Rao, K.M.1
  • 321
    • 3042722927 scopus 로고
    • Resolvents, transition functions and strongly Markovian processes
    • RAY, D. B. Resolvents, transition functions and strongly Markovian processes, Ann. Math., 70, 43-72 (1959).
    • (1959) Ann. Math , vol.70 , pp. 43-72
    • Ray, D.B.1
  • 322
    • 84972512714 scopus 로고
    • Sojourn times of a diffusion process
    • RAY, D. B. Sojourn times of a diffusion process, Illinois J. Math., 7, 615-630 (1963).
    • (1963) Illinois J. Math , vol.7 , pp. 615-630
    • Ray, D.B.1
  • 323
    • 0038230579 scopus 로고
    • Denumerable Markov processes, II
    • REUTER, G. E. H. Denumerable Markov processes, II, J. London Math. Soc., 34, 81-91 (1959).
    • (1959) J. London Math. Soc , vol.34 , pp. 81-91
    • Reuter, G.E.H.1
  • 324
    • 84953242314 scopus 로고
    • The Martin boundary of a recurrent random walk has one or two points
    • American Mathematical Society, Providence, RI
    • REVUZ, D. The Martin boundary of a recurrent random walk has one or two points, in Probability: Proc. Symp. Pure Math. XXXI, American Mathematical Society, Providence, RI, 1977, pp. 125-130.
    • (1977) Probability: Proc. Symp. Pure Math. XXXI , pp. 125-130
    • Revuz, D.1
  • 325
    • 0010265665 scopus 로고
    • Williams’ characterization of the Brownian excursion law: Proof and applications
    • Springer, Berlin
    • ROGERS, L. C. G. Williams’ characterization of the Brownian excursion law: proof and applications, Séminaire de Probabilités XV: Lecture Notes in Mathematics 850, Springer, Berlin, 1981, pp. 227-250.
    • (1981) Séminaire de Probabilités XV: Lecture Notes in Mathematics 850 , pp. 227-250
    • Rogers, L.C.G.1
  • 326
    • 0000649226 scopus 로고
    • Itô excursion theory via resolvents
    • ROGERS, L. C. G. Itô excursion theory via resolvents, Z. Wahrscheinlichkeitstheorie, 63, 237-255 (1983).
    • (1983) Z. Wahrscheinlichkeitstheorie , vol.63 , pp. 237-255
    • Rogers, L.C.G.1
  • 327
    • 0001171076 scopus 로고
    • Smooth transition densities for one-dimensional diffusions
    • ROGERS, L. C. G. Smooth transition densities for one-dimensional diffusions, Bull. London Math. Soc., 17, 157-161 (1985).
    • (1985) Bull. London Math. Soc , vol.17 , pp. 157-161
    • Rogers, L.C.G.1
  • 329
    • 0001518466 scopus 로고
    • A local time approach to self-intersections of Brownian paths in space
    • ROSEN, J. A local time approach to self-intersections of Brownian paths in space, Comm. Math. Phys., 88, 327-338 (1983).
    • (1983) Comm. Math. Phys , vol.88 , pp. 327-338
    • Rosen, J.1
  • 330
    • 23644440327 scopus 로고
    • Géometrie différentielle du 2ième ordre, semimartingales et équations différentielles stochastiques sur une variété différentielle
    • Springer, Berlin
    • SCHWARTZ, L. Géometrie différentielle du 2ième ordre, semimartingales et équations différentielles stochastiques sur une variété différentielle, Sém. de Probabilités XVI: Supplément, Lecture Notes in Mathematics 921, Springer, Berlin, 1982, pp. 1-148.
    • (1982) Sém. de Probabilités XVI: Supplément, Lecture Notes in Mathematics 921 , pp. 1-148
    • Schwartz, L.1
  • 331
    • 84953242015 scopus 로고    scopus 로고
    • Forthcoming book on Markov processes
    • SHARPE, M. J. Forthcoming book on Markov processes.
    • Sharpe, M.J.1
  • 332
    • 84959812950 scopus 로고
    • On the Ray-Knight property of local times
    • SHEPPARD, P. On the Ray-Knight property of local times, J. London Math. Soc., 31, 377-384 (1985).
    • (1985) J. London Math. Soc , vol.31 , pp. 377-384
    • Sheppard, P.1
  • 333
    • 0002115073 scopus 로고
    • Bessel diffusions as a one-parameter family of diffusion processes
    • SHIGA, T. and WATANABE, S. Bessel diffusions as a one-parameter family of diffusion processes, Z. Wahrscheinlichkeitstheorie, 27, 37-46 (1973).
    • (1973) Z. Wahrscheinlichkeitstheorie , vol.27 , pp. 37-46
    • Shiga, T.1    Watanabe, S.2
  • 334
    • 0001365070 scopus 로고
    • Derivatives of Wiener functionals and absolute continuity of induced measure
    • SHIGEKAWA, I. Derivatives of Wiener functionals and absolute continuity of induced measure J Math. Kyoto Univ., 20, 263-289 (1980).
    • (1980) J Math. Kyoto Univ , vol.20 , pp. 263-289
    • Shigekawa, I.1
  • 339
    • 0001380311 scopus 로고
    • Limit theorems for stochastic processes
    • SKOROKHOD, A. V. Limit theorems for stochastic processes, Theor. Prob. Applic., 1, 261-290 (1956).
    • (1956) Theor. Prob. Applic , vol.1 , pp. 261-290
    • Skorokhod, A.V.1
  • 340
    • 84883020713 scopus 로고
    • Limit theorems for Markov processes
    • SKOROKHOD, A. V. Limit theorems for Markov processes, Theor. Prob. Applic., 3, 202-246 (1958).
    • (1958) Theor. Prob. Applic , vol.3 , pp. 202-246
    • Skorokhod, A.V.1
  • 342
    • 0000187772 scopus 로고
    • An invariance principle for the law of the iterated logarithm
    • STRASSEN, V. An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie, 3, 211-226 (1964).
    • (1964) Z. Wahrscheinlichkeitstheorie , vol.3 , pp. 211-226
    • Strassen, V.1
  • 343
    • 0000571608 scopus 로고
    • Almost sure behaviour of sums of independent random variables and martingales
    • Vol. 2, Part 1, University of California Press
    • STRASSEN, V. Almost sure behaviour of sums of independent random variables and martingales, Proc. 5th Berkeley Symp. Math. Statist. Prob., Vol. 2, Part 1, University of California Press, 1966, pp. 315-343.
    • (1966) Proc. 5th Berkeley Symp. Math. Statist. Prob , pp. 315-343
    • Strassen, V.1
  • 344
    • 0011661171 scopus 로고
    • The Malliavin calculus and its applications to second-order parabolic differential operators I, II
    • STROOCK, D. W. The Malliavin calculus and its applications to second-order parabolic differential operators I, II, Math. System Theory, 14, 25-65, 141-171 (1981).
    • (1981) Math. System Theory , vol.14
    • Stroock, D.W.1
  • 345
    • 0000989873 scopus 로고
    • The Malliavin calculus; a functional analytical approach
    • STROOCK, D. W. The Malliavin calculus; a functional analytical approach, J. Fund. Anal., 44, 217-257 (1981).
    • (1981) J. Fund. Anal , vol.44 , pp. 217-257
    • Stroock, D.W.1
  • 346
    • 0000775921 scopus 로고
    • Diffusion processes associated with Lévy generators
    • STROOCK, D. W. Diffusion processes associated with Lévy generators, Z. Wahrscheinlichkeitstheorie, 32, 209-244 (1975).
    • (1975) Z. Wahrscheinlichkeitstheorie , vol.32 , pp. 209-244
    • Stroock, D.W.1
  • 349
    • 0000395295 scopus 로고
    • On the support of diffusion processes with applications to the strong maximum principle
    • Ill, Univ. Calif. Press, Berkeley
    • STROOCK, D. W. and VARADHAN, S. R. S. On the support of diffusion processes with applications to the strong maximum principle, Proc. 6th Berkeley Symp. Math. Statist. Prob., Ill, Univ. Calif. Press, Berkeley, 1972, pp. 333-359.
    • (1972) Proc. 6th Berkeley Symp. Math. Statist. Prob , pp. 333-359
    • Stroock, D.W.1    Varadhan, S.R.S.2
  • 350
    • 84980153169 scopus 로고
    • Diffusion processes with boundary conditions
    • STROOCK, D. W. and VARADHAN, S. R. S. Diffusion processes with boundary conditions, Comm. Pure Appl. Math., 24, 147-225 (1971).
    • (1971) Comm. Pure Appl. Math , vol.24 , pp. 147-225
    • Stroock, D.W.1    Varadhan, S.R.S.2
  • 352
    • 0002801174 scopus 로고
    • On the gap between deterministic and stochastic ordinary differential equations
    • SUSSMANN, H. J. On the gap between deterministic and stochastic ordinary differential equations, Ann. Prob., 6, 19-41 (1978).
    • (1978) Ann. Prob , vol.6 , pp. 19-41
    • Sussmann, H.J.1
  • 353
    • 0039008804 scopus 로고
    • A stopped Brownian motion formula
    • TAYLOR, H. M. A stopped Brownian motion formula, Ann. Prob., 3, 234-246 (1975).
    • (1975) Ann. Prob , vol.3 , pp. 234-246
    • Taylor, H.M.1
  • 354
    • 0038433594 scopus 로고
    • Sample path properties of processes with stationary independent increments
    • eds D. G. Kendall and E. F. Harding, Wiley, New York
    • TAYLOR, S. J. Sample path properties of processes with stationary independent increments, in Stochastic Analysis, eds D. G. Kendall and E. F. Harding, Wiley, New York, 1973, pp. 387-414.
    • (1973) Stochastic Analysis , pp. 387-414
    • Taylor, S.J.1
  • 355
    • 0040060883 scopus 로고
    • An example of the stochastic equation having no strong solution
    • TSIRELSON, B. S. An example of the stochastic equation having no strong solution, Teoria Verojatn. i Primenen., 20, (2), 427-430 (1975).
    • (1975) Teoria Verojatn. i Primenen , vol.20 , Issue.2 , pp. 427-430
    • Tsirelson, B.S.1
  • 357
    • 0003324465 scopus 로고
    • Large deviations and applications
    • Philadelphia
    • VARADHAN, S. R. S. Large deviations and applications, SIAM, Philadelphia, 1984.
    • (1984) SIAM
    • Varadhan, S.R.S.1
  • 361
    • 0002625443 scopus 로고
    • On discontinuous additive functionals and Lévy measures of a Markov process
    • WATANABE, S. On discontinuous additive functionals and Lévy measures of a Markov process, Jap. J. Math., 34, 53-79 (1964).
    • (1964) Jap. J. Math , vol.34 , pp. 53-79
    • Watanabe, S.1
  • 364
    • 84953205905 scopus 로고
    • Brownian motions and diffusions as Markov processes
    • WILLIAMS, D. Brownian motions and diffusions as Markov processes, Bull. London Math. Soc., 6, 257-303 (1974).
    • (1974) Bull. London Math. Soc , vol.6 , pp. 257-303
    • Williams, D.1
  • 365
    • 0011361829 scopus 로고
    • Some basic theorems on harnesses
    • eds. D. G. Kendall and E. F. Harding, Wiley, New York
    • WILLIAMS, D. Some basic theorems on harnesses, in Stochastic Analysis, eds. D. G. Kendall and E. F. Harding, Wiley, New York, 1973, pp. 349-366.
    • (1973) Stochastic Analysis , pp. 349-366
    • Williams, D.1
  • 366
    • 33846489127 scopus 로고
    • On Lévy’s downcrossing theorem
    • WILLIAMS, D. On Lévy’s downcrossing theorem, Z. fVahrscheinlichkeitstheorie, 40, 157-158 (1977).
    • (1977) Z. fVahrscheinlichkeitstheorie , vol.40 , pp. 157-158
    • Williams, D.1
  • 367
    • 33749017547 scopus 로고
    • Path decomposition and continuity of local time for one-dimensional diffusions, I
    • Ser. 3
    • WILLIAMS, D. WILLIAMS, D. Path decomposition and continuity of local time for one-dimensional diffusions, I, Proc. London Math. Soc., Ser. 3, 28, 738-768 (1974).
    • (1974) Proc. London Math. Soc , vol.28 , pp. 738-768
    • Williams, D.1    Williams, D.2
  • 369
    • 84968487174 scopus 로고
    • Markov properties of Brownian local time
    • WILLIAMS, D. Markov properties of Brownian local time, Bull. Am. Math. Soc., 75, 1035-1036 (1969).
    • (1969) Bull. Am. Math. Soc , vol.75 , pp. 1035-1036
    • Williams, D.1
  • 370
    • 84966207775 scopus 로고
    • Decomposing the Brownian path
    • WILLIAMS, D. Decomposing the Brownian path, Bull. Am. Math. Soc., 76, 871-873 (1970).
    • (1970) Bull. Am. Math. Soc , vol.76 , pp. 871-873
    • Williams, D.1
  • 371
    • 84953263870 scopus 로고
    • The Q-matrix problem for Markov chains
    • WILLIAMS, D. The Q-matrix problem for Markov chains, Bull. Am. Math. Soc., 81, 1115-1118 (1975).
    • (1975) Bull. Am. Math. Soc , vol.81 , pp. 1115-1118
    • Williams, D.1
  • 373
    • 0007024709 scopus 로고
    • A note on the Q-matrices of Markov chains
    • WILLIAMS, D. A note on the Q-matrices of Markov chains, Z. Wahrscheinlichkeitstheorie, 7, 116-121 (1967).
    • (1967) Z. Wahrscheinlichkeitstheorie , vol.7 , pp. 116-121
    • Williams, D.1
  • 374
    • 84953261074 scopus 로고
    • Some 2-matrix problems
    • American Mathematical Society, Providence, RI
    • WILLIAMS, D. Some 2-matrix problems, in Probability: Proc. Symp. Pure Math. XXXI, American Mathematical Society, Providence, RI, 1977, pp. 165-169.
    • (1977) Probability: Proc. Symp. Pure Math. XXXI , pp. 165-169
    • Williams, D.1
  • 378
    • 0012269578 scopus 로고
    • On a comparison theorem for solutions of stochastic differential equations and its applications
    • YAMADA, T. On a comparison theorem for solutions of stochastic differential equations and its applications, J. Math. Kyoto Univ., 13, 497-512 (1973).
    • (1973) J. Math. Kyoto Univ , vol.13 , pp. 497-512
    • Yamada, T.1
  • 379
    • 0002171410 scopus 로고
    • On the strong comparison theorems for solutions of stochastic differential equations
    • YAMADA, T. and OGURA, Y. On the strong comparison theorems for solutions of stochastic differential equations, Z. fVahrscheinlichkeitstheorie, 56, 3-19 (1981).
    • (1981) Z. fVahrscheinlichkeitstheorie , vol.56 , pp. 3-19
    • Yamada, T.1    Ogura, Y.2
  • 380
    • 0000827166 scopus 로고
    • On the uniqueness of solutions of stochastic differential equations
    • YAMADA, T. and WATANABE, S. On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ., 11, 155-167 (1971).
    • (1971) J. Math. Kyoto Univ , vol.11 , pp. 155-167
    • Yamada, T.1    Watanabe, S.2
  • 386
    • 84972498079 scopus 로고
    • Brownian motion in homogeneous Riemannian space
    • YOSIDA, K. Brownian motion in homogeneous Riemannian space, Pacific J. Math., 2, 263-296 (1952).
    • (1952) Pacific J. Math , vol.2 , pp. 263-296
    • Yosida, K.1
  • 387
    • 0039493335 scopus 로고
    • The Malliavin calculus
    • ZAKAI, M. The Malliavin calculus, Acta Appl. Math., 3, 175-207 (1985).
    • (1985) Acta Appl. Math , vol.3 , pp. 175-207
    • Zakai, M.1
  • 389
    • 84957165179 scopus 로고
    • A transformation of the phase space of a diffusion process that removes the drift
    • ZVONKIN, A. K. A transformation of the phase space of a diffusion process that removes the drift, Math. USSR Sbornik, 22, 129-149 (1974).
    • (1974) Math. USSR Sbornik , vol.22 , pp. 129-149
    • Zvonkin, A.K.1


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