메뉴 건너뛰기




Volumn 9, Issue 1, 2003, Pages 1-24

Hitting, occupation and inverse local times of one-dimensional diffusions: Martingale and excursion approaches

Author keywords

Arcsine law; Feynman Kac formula; Last exit decomposition

Indexed keywords


EID: 21244501196     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1068129008     Document Type: Article
Times cited : (61)

References (48)
  • 1
    • 0001465651 scopus 로고
    • Une extension multidimensionnelle de la loi de l'arc sinus
    • J. Azéma, P.A. Meyer and M. Yor (eds), Lecture Notes in Math. 1372, Berlin: Springer-Verlag
    • Barlow, M., Pitman, J. and Yor, M. (1989) Une extension multidimensionnelle de la loi de l'arc sinus. In J. Azéma, P.A. Meyer and M. Yor (eds), Séminaire de Probabilités XXIII, Lecture Notes in Math. 1372, pp. 294-314. Berlin: Springer-Verlag.
    • (1989) Séminaire de Probabilités , vol.23 , pp. 294-314
    • Barlow, M.1    Pitman, J.2    Yor, M.3
  • 3
    • 0037504682 scopus 로고
    • Comparaison entre temps d'atteinte et temps de séjour de certaines diffusions réelles
    • J. Azéma and M. Yor (eds), Lecture Notes in Math. 1123, Berlin: Springer-Verlag
    • Biane, P. (1985) Comparaison entre temps d'atteinte et temps de séjour de certaines diffusions réelles. In J. Azéma and M. Yor (eds), Séminaire de Probabilités XIX, Lecture Notes in Math. 1123, pp. 291-296. Berlin: Springer-Verlag.
    • (1985) Séminaire de Probabilités , vol.19 , pp. 291-296
    • Biane, P.1
  • 4
    • 0035599225 scopus 로고    scopus 로고
    • Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions
    • Biane, P., Pitman, J. and Yor, M. (2001) Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions. Bull. Amer. Math. Soc., 38, 435-465.
    • (2001) Bull. Amer. Math. Soc. , vol.38 , pp. 435-465
    • Biane, P.1    Pitman, J.2    Yor, M.3
  • 5
    • 0002306415 scopus 로고
    • Last exit decompositions and regularity at the boundary of transition probabilities
    • Bismut, J.-M. (1985) Last exit decompositions and regularity at the boundary of transition probabilities. Z. Wahrscheinlichkeitstheorie Verw. Geb., 69, 65-98.
    • (1985) Z. Wahrscheinlichkeitstheorie Verw. Geb. , vol.69 , pp. 65-98
    • Bismut, J.-M.1
  • 7
    • 84968478877 scopus 로고
    • First passage times and sojourn density for Brownian motion in space and the exact Hausdorff measure of the sample path
    • Ciesielski, Z. and Taylor, S.J. (1962) First passage times and sojourn density for Brownian motion in space and the exact Hausdorff measure of the sample path. Trans. Amer. Math. Soc., 103, 434-450.
    • (1962) Trans. Amer. Math. Soc. , vol.103 , pp. 434-450
    • Ciesielski, Z.1    Taylor, S.J.2
  • 8
    • 0001010150 scopus 로고
    • On the joint distribution of the maximum and its location for a linear diffusion
    • Csáki, E., Földes, A. and Salminen, P. (1987) On the joint distribution of the maximum and its location for a linear diffusion. Ann. Inst. H. Poincaré Probab. Statist., 23, 179-194.
    • (1987) Ann. Inst. H. Poincaré Probab. Statist. , vol.23 , pp. 179-194
    • Csáki, E.1    Földes, A.2    Salminen, P.3
  • 11
    • 33747361513 scopus 로고
    • Another look at Williams' decomposition theorem
    • E. Çinlar, K.L. Chung, R.K. Getoor and J. Glover (eds), Progr. Probab. Statist. 12, Boston: Birkhäuser
    • Fitzsimmons, P.J. (1986) Another look at Williams' decomposition theorem. In E. Çinlar, K.L. Chung, R.K. Getoor and J. Glover (eds), Seminar on Stochastic Processes 1985, Progr. Probab. Statist. 12, pp. 79-85. Boston: Birkhäuser.
    • (1986) Seminar on Stochastic Processes 1985 , pp. 79-85
    • Fitzsimmons, P.J.1
  • 12
    • 0042511806 scopus 로고
    • Last exit decompositions and distributions
    • Getoor, R.K. and Sharpe, M.J. (1973a) Last exit decompositions and distributions. Indiana Univ. Math. J., 23, 377-404.
    • (1973) Indiana Univ. Math. J. , vol.23 , pp. 377-404
    • Getoor, R.K.1    Sharpe, M.J.2
  • 13
    • 0041510028 scopus 로고
    • Last exit times and additive functionals
    • Getoor, R.K. and Sharpe, M.J. (1973b) Last exit times and additive functionals. Ann. Probab., 1, 550-569.
    • (1973) Ann. Probab. , vol.1 , pp. 550-569
    • Getoor, R.K.1    Sharpe, M.J.2
  • 15
    • 0001327573 scopus 로고
    • Fluctuation identities for Lévy processes and splitting at the maximum
    • Greenwood, P. and Pitman, J. (1980) Fluctuation identities for Lévy processes and splitting at the maximum. Adv. in Appl. Probab., 12, 893-902.
    • (1980) Adv. in Appl. Probab. , vol.12 , pp. 893-902
    • Greenwood, P.1    Pitman, J.2
  • 16
    • 0001050284 scopus 로고
    • Poisson point processes attached to Markov processes
    • L. LeCam, J. Neyman and E.L. Scott (eds), Berkeley: University of California Press
    • Itô, K. (1972) Poisson point processes attached to Markov processes. In L. LeCam, J. Neyman and E.L. Scott (eds), Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 3, pp. 225-240. Berkeley: University of California Press.
    • (1972) Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability , vol.3 , pp. 225-240
    • Itô, K.1
  • 18
    • 32144438653 scopus 로고
    • Transformation of Markov processes by multiplicative functionals
    • Itô, K. and Watanabe, S. (1965) Transformation of Markov processes by multiplicative functionals. Ann. Inst. Fourier (Grenoble), 15(1), 13-30.
    • (1965) Ann. Inst. Fourier (Grenoble) , vol.15 , Issue.1 , pp. 13-30
    • Itô, K.1    Watanabe, S.2
  • 19
    • 0009153241 scopus 로고    scopus 로고
    • The Feynman-Kac formula and decomposition of Brownian paths
    • Jeanblanc, M., Pitman, J. and Yor, M. (1997) The Feynman-Kac formula and decomposition of Brownian paths. Comput. Appl. Math., 16, 27-52.
    • (1997) Comput. Appl. Math. , vol.16 , pp. 27-52
    • Jeanblanc, M.1    Pitman, J.2    Yor, M.3
  • 20
    • 0036065413 scopus 로고    scopus 로고
    • Self-similar processes with independent increments associated with Lévy and Bessel processes
    • Jeanblanc, M., Pitman, J. and Yor, M. (2002) Self-similar processes with independent increments associated with Lévy and Bessel processes. Stochastic Process. Appl., 100, 223-231.
    • (2002) Stochastic Process. Appl. , vol.100 , pp. 223-231
    • Jeanblanc, M.1    Pitman, J.2    Yor, M.3
  • 21
    • 0003021436 scopus 로고
    • On some connections between probability theory and differential and integral equations
    • J. Neyman (ed.), Berkeley: University of California Press
    • Kac, M. (1951) On some connections between probability theory and differential and integral equations. In J. Neyman (ed.), Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 189-215. Berkeley: University of California Press.
    • (1951) Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability , pp. 189-215
    • Kac, M.1
  • 22
    • 0001251792 scopus 로고
    • Some probabilistic properties of Bessel functions
    • Kent, J. (1978) Some probabilistic properties of Bessel functions. Ann. Probab., 6, 760-770.
    • (1978) Ann. Probab. , vol.6 , pp. 760-770
    • Kent, J.1
  • 23
    • 0542399424 scopus 로고
    • Eigenvalue expansions for diffusion hitting times
    • Kent, J.T. (1980) Eigenvalue expansions for diffusion hitting times. Z. Wahrscheinlichkeitstheorie Verw. Geb., 52 309-319.
    • (1980) Z. Wahrscheinlichkeitstheorie Verw. Geb. , vol.52 , pp. 309-319
    • Kent, J.T.1
  • 24
    • 7444264106 scopus 로고
    • The spectral decomposition of a diffusion hitting time
    • Kent, J.T. (1982) The spectral decomposition of a diffusion hitting time. Ann. Probab., 10, 207-219.
    • (1982) Ann. Probab. , vol.10 , pp. 207-219
    • Kent, J.T.1
  • 26
    • 0000518144 scopus 로고
    • Exit systems
    • Maisonneuve, B. (1975) Exit systems. Ann. Probab., 3, 399-411.
    • (1975) Ann. Probab. , vol.3 , pp. 399-411
    • Maisonneuve, B.1
  • 27
    • 4243882935 scopus 로고
    • Application du calcul stochastique à l'étude de processus de Markov réguliers sur [0,1]
    • Méléard, S. (1986) Application du calcul stochastique à l'étude de processus de Markov réguliers sur [0,1]. Stochastics Stochastic Rep., 19(1-2), 41-82.
    • (1986) Stochastics Stochastic Rep. , vol.19 , Issue.1-2 , pp. 41-82
    • Méléard, S.1
  • 28
    • 0346113963 scopus 로고
    • Processus de Poisson ponctuels, d'après K. Itô
    • Lecture Notes in Math. 191, Berlin: Springer-Verlag. Erratum (1972) in Séminaire de Probabilités VI, Lecture Notes in Math. 258, pp. 253
    • Meyer, P.A. (1971) Processus de Poisson ponctuels, d'après K. Itô. In Séminaire de Probabilités V, Lecture Notes in Math. 191, pp. 177-190. Berlin: Springer-Verlag. Erratum (1972) in Séminaire de Probabilités VI, Lecture Notes in Math. 258, pp. 253.
    • (1971) Séminaire de Probabilités , vol.5 , pp. 177-190
    • Meyer, P.A.1
  • 29
    • 0039475211 scopus 로고
    • Stationary excursions
    • J. Azéma, P.A. Meyer and M. Yor (eds), Lecture Notes in Math. 1247, Berlin: Springer-Verlag
    • Pitman, J. (1987) Stationary excursions. In J. Azéma, P.A. Meyer and M. Yor (eds), Séminaire de Probabilités XXI, Lecture Notes in Math. 1247, pp. 289-302. Berlin: Springer-Verlag.
    • (1987) Séminaire de Probabilités , vol.21 , pp. 289-302
    • Pitman, J.1
  • 30
    • 0001452295 scopus 로고
    • Bessel processes and infinitely divisible laws
    • D. Williams (ed.), Lecture Notes in Math. 851, Berlin: Springer-Verlag
    • Pitman, J. and Yor, M. (1981) Bessel processes and infinitely divisible laws. In D. Williams (ed.), Stochastic Integrals, Lecture Notes in Math. 851, pp. 285-370. Berlin: Springer-Verlag.
    • (1981) Stochastic Integrals , pp. 285-370
    • Pitman, J.1    Yor, M.2
  • 32
    • 0000030777 scopus 로고
    • Asymptotic laws of planar Brownian motion
    • Pitman, J. and Yor, M. (1986) Asymptotic laws of planar Brownian motion. Ann. Probab., 14, 733-779.
    • (1986) Ann. Probab. , vol.14 , pp. 733-779
    • Pitman, J.1    Yor, M.2
  • 33
    • 0002975171 scopus 로고    scopus 로고
    • Decomposition at the maximum for excursions and bridges of one-dimensional diffusions
    • N. Ikeda, S. Watanabe, M. Fukushima and H. Kunita (eds), Tokyo: Springer-Verlag
    • Pitman, J. and Yor, M. (1996) Decomposition at the maximum for excursions and bridges of one-dimensional diffusions. In N. Ikeda, S. Watanabe, M. Fukushima and H. Kunita (eds), Itô's Stochastic Calculus and Probability Theory, pp. 293-310. Tokyo: Springer-Verlag.
    • (1996) Itô's Stochastic Calculus and Probability Theory , pp. 293-310
    • Pitman, J.1    Yor, M.2
  • 34
    • 0001374067 scopus 로고    scopus 로고
    • On the lengths of excursions of some Markov processes
    • J. Azéma, M. Emery and M. Yor (eds), Lecture Notes in Math. 1655, Berlin: Springer-Verlag
    • Pitman, J. and Yor, M. (1997) On the lengths of excursions of some Markov processes. In J. Azéma, M. Emery and M. Yor (eds), Séminaire de Probabilités XXXI, Lecture Notes in Math. 1655, pp. 272-286, Berlin: Springer-Verlag.
    • (1997) Séminaire de Probabilités , vol.31 , pp. 272-286
    • Pitman, J.1    Yor, M.2
  • 35
    • 0007433243 scopus 로고    scopus 로고
    • Laplace transforms related to excursions of a one-dimensional diffusion
    • Pitman, J. and Yor, M. (1999) Laplace transforms related to excursions of a one-dimensional diffusion. Bernoulli, 5, 249-255.
    • (1999) Bernoulli , vol.5 , pp. 249-255
    • Pitman, J.1    Yor, M.2
  • 38
    • 0347706584 scopus 로고    scopus 로고
    • On last exit decompositions of linear diffusions
    • Salminen, P. (1997) On last exit decompositions of linear diffusions. Studia Sci. Math. Hungar., 33 (1-3), 251-262.
    • (1997) Studia Sci. Math. Hungar. , vol.33 , Issue.1-3 , pp. 251-262
    • Salminen, P.1
  • 39
    • 33747373785 scopus 로고
    • A generalised arc-sine law and Nelson's stochastic mechanics of one-dimensional time homogeneous diffusions
    • M.A. Pinsky (ed.), Progr. Probab. 22, Boston: Birkhäuser
    • Truman, A. and Williams, D. (1990) A generalised arc-sine law and Nelson's stochastic mechanics of one-dimensional time homogeneous diffusions. In M.A. Pinsky (ed.), Diffusion Processes and Related Problems in Analysis, Vol. 1, Progr. Probab. 22, pp. 117-135. Boston: Birkhäuser.
    • (1990) Diffusion Processes and Related Problems in Analysis , vol.1 , pp. 117-135
    • Truman, A.1    Williams, D.2
  • 40
    • 33747357725 scopus 로고
    • An elementary formula for Poisson-Lévy excursion measures for one-dimensional time-homogeneous processes
    • A. Truman and I.M. Davies (eds) Singapore: World Scientific
    • Truman, A. and Williams, D. (1992) An elementary formula for Poisson-Lévy excursion measures for one-dimensional time-homogeneous processes. In A. Truman and I.M. Davies (eds) Stochastics and Quantum Mechanics, pp. 238-247. Singapore: World Scientific.
    • (1992) Stochastics and Quantum Mechanics , pp. 238-247
    • Truman, A.1    Williams, D.2
  • 41
    • 0141643470 scopus 로고
    • Schrödinger operators and asymptotics for Poisson-Lévy excursion measures for one-dimensional time-homogeneous diffusions
    • M.C. Cranston and M.A. Pinsky (eds), Proc. Sympos. Pure Math. 57, Providence, RI: American Mathematical Society
    • Truman, A., Williams, D. and Yu, K.Y. (1995) Schrödinger operators and asymptotics for Poisson-Lévy excursion measures for one-dimensional time-homogeneous diffusions. In M.C. Cranston and M.A. Pinsky (eds), Stochastic Analysis, Proc. Sympos. Pure Math. 57, pp. 145-156. Providence, RI: American Mathematical Society.
    • (1995) Stochastic Analysis , pp. 145-156
    • Truman, A.1    Williams, D.2    Yu, K.Y.3
  • 42
    • 0000893434 scopus 로고
    • Generalized are-sine laws for one-dimensional diffusion processes and random walks
    • M.C. Cranston and M.A. Pinsky (eds), Proc. Sympos. Pure Math. 57, Providence, RI: American Mathematical Society
    • Watanabe, S. (1995) Generalized are-sine laws for one-dimensional diffusion processes and random walks. In M.C. Cranston and M.A. Pinsky (eds), Stochastic Analysis, Proc. Sympos. Pure Math. 57, pp. 157-172. Providence, RI: American Mathematical Society.
    • (1995) Stochastic Analysis , pp. 157-172
    • Watanabe, S.1
  • 43
    • 33747352209 scopus 로고
    • Explicit formulas for the distribution of sojourn times of one-dimensional diffusions
    • Weber, M. (1994) Explicit formulas for the distribution of sojourn times of one-dimensional diffusions. Wiss. Z. Tech. Univ. Dresden, 43(2), 9-11.
    • (1994) Wiss. Z. Tech. Univ. Dresden , vol.43 , Issue.2 , pp. 9-11
    • Weber, M.1
  • 44
    • 33749017547 scopus 로고
    • Path decomposition and continuity of local time for one dimensional diffusions i
    • Williams, D. (1974) Path decomposition and continuity of local time for one dimensional diffusions I. Proc. London Math. Soc. (3), 28, 738-768.
    • (1974) Proc. London Math. Soc. (3) , vol.28 , pp. 738-768
    • Williams, D.1
  • 45
    • 0040708448 scopus 로고
    • Une explication du théorème de Ciesielski-Taylor
    • Yor, M. (1991) Une explication du théorème de Ciesielski-Taylor. Ann. Inst. H. Poincaré Probab. Statist., 27, 201-213.
    • (1991) Ann. Inst. H. Poincaré Probab. Statist. , vol.27 , pp. 201-213
    • Yor, M.1
  • 47
    • 0007195242 scopus 로고
    • Local times and excursions for brownian motion: A concise introduction
    • Caracas: Postgrado de Matemáticas, Facultad de Ciencias, Universidad Central de Venezuela
    • Yor, M. (1995) Local Times and Excursions for Brownian Motion: A Concise Introduction, volume 1 of Lecciones en Matemáticas. Caracas: Postgrado de Matemáticas, Facultad de Ciencias, Universidad Central de Venezuela.
    • (1995) Lecciones en Matemáticas , vol.1
    • Yor, M.1
  • 48
    • 0001709245 scopus 로고
    • A transformation of the phase space of a diffusion process that will remove the drift
    • Zvonkin, A.K. (1974) A transformation of the phase space of a diffusion process that will remove the drift. Mat. Sb. (N.S.), 93(135), 129-149, 152.
    • (1974) Mat. Sb. (N.S.) , vol.93 , Issue.135 , pp. 129-149
    • Zvonkin, A.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.