메뉴 건너뛰기




Volumn 1, Issue 1, 2004, Pages 321-392

The Skorokhod embedding problem and its offspring

Author keywords

Az ma yor embedding; Chacon walsh embedding; One dimensional potential theory; Optimal stopping; Root embedding; Skorokhod embedding problem; Stopping times

Indexed keywords


EID: 84890634099     PISSN: None     EISSN: 15495787     Source Type: Journal    
DOI: 10.1214/154957804100000060     Document Type: Article
Times cited : (230)

References (127)
  • 1
    • 84931965296 scopus 로고
    • Une nouvelle représentation du type de Skorokhod
    • Lecture Notes in Math., Springer, Berlin, MR373026
    • J. Azéma and P. A. Meyer. Une nouvelle représentation du type de Skorokhod. In Séminaire de Probabilités, VIII, pages 1-10. Lecture Notes in Math., Vol. 381. Springer, Berlin, 1974. MR373026
    • (1974) Séminaire de Probabilités, VIII , vol.381 , pp. 1-10
    • Azéma, J.1    Meyer, P.A.2
  • 2
    • 0002483109 scopus 로고
    • Le problème de Skorokhod: compléments à \Une solution simple au problème de Skorokhod"
    • of Lecture Notes in Math., Springer, Berlin, MR544832
    • J. Azéma and M. Yor. Le problème de Skorokhod: compléments à "Une solution simple au problème de Skorokhod". In Séminaire de Probabilités, XIII, volume 721 of Lecture Notes in Math., pages 625-633. Springer, Berlin, 1979. MR544832
    • (1979) Séminaire de Probabilités, XIII , vol.721 , pp. 625-633
    • Azéma, J.1    Yor, M.2
  • 3
    • 0002483109 scopus 로고
    • Une solution simple au problème de Skorokhod
    • of Lecture Notes in Math., Springer, Berlin, MR544782
    • J. Azéma and M. Yor. Une solution simple au problème de Skorokhod. In Séminaire de Probabilités, XIII, volume 721 of Lecture Notes in Math., pages 90-115. Springer, Berlin, 1979. MR544782
    • (1979) Séminaire de Probabilités, XIII , vol.721 , pp. 90-115
    • Azéma, J.1    Yor, M.2
  • 4
    • 0013210195 scopus 로고
    • Skorokhod imbedding via stochastic integrals
    • of Lecture Notes in Math.,Springer, Berlin, MR770414
    • R. F. Bass. Skorokhod imbedding via stochastic integrals. In Séminaire de Probabilités, XVII, volume 986 of Lecture Notes in Math., pages 221-224. Springer, Berlin, 1983. MR770414
    • (1983) Séminaire de Probabilités, XVII , vol.986 , pp. 221-224
    • Bass, R.F.1
  • 5
    • 84972536239 scopus 로고
    • Potentials of stopped distributions
    • MR358960
    • J. R. Baxter and R. V. Chacon. Potentials of stopped distributions. Illinois J. Math., 18:649-656, 1974. MR358960
    • (1974) Illinois J. Math. , vol.18 , pp. 649-656
    • Baxter, J.R.1    Chacon, R.V.2
  • 6
    • 0013211983 scopus 로고
    • Representation of measures by balayage from a regular recurrent point
    • MR1143434
    • J. Bertoin and Y. Le Jan. Representation of measures by balayage from a regular recurrent point. Ann. Probab., 20(1):538-548, 1992. MR1143434
    • (1992) Ann. Probab. , vol.20 , Issue.1 , pp. 538-548
    • Bertoin, J.1    Le Jan, Y.2
  • 8
    • 84972508275 scopus 로고
    • A converse to the dominated convergence theorem
    • MR151572
    • D. Blackwell and L. E. Dubins. A converse to the dominated convergence theorem. Illinois J. Math., 7:508-514, 1963. MR151572
    • (1963) Illinois J. Math. , vol.7 , pp. 508-514
    • Blackwell, D.1    Dubins, L.E.2
  • 9
    • 0010682521 scopus 로고
    • Markov processes and potential theory
    • Academic Press, New York, MR264757
    • R. M. Blumenthal and R. K. Getoor. Markov processes and potential theory. Pure and Applied Mathematics, Vol. 29. Academic Press, New York, 1968. MR264757
    • (1968) Pure and Applied Mathematics , vol.29
    • Blumenthal, R.M.1    Getoor, R.K.2
  • 10
    • 0002181147 scopus 로고
    • First exit times from a square root boundary
    • (Berkeley, Calif., 1965/66), Vol. II: Contributions to Probability Theory, Part 2, pages 9- 16. Univ. California Press, Berkeley, Calif., MR212865
    • L. Breiman. First exit times from a square root boundary. In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II: Contributions to Probability Theory, Part 2, pages 9- 16. Univ. California Press, Berkeley, Calif., 1967. MR212865
    • (1967) In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability
    • Breiman, L.1
  • 12
    • 84890675804 scopus 로고
    • Une remarque sur le problème de Skorokhod
    • Lecture Notes in Math., Springer, Berlin, MR368193
    • J. Bretagnolle. Une remarque sur le problème de Skorokhod. In Séminaire de Probabilités, VIII, pages 11-19. Lecture Notes in Math., Vol. 381. Springer, Berlin, 1974. MR368193
    • (1974) In Séminaire de Probabilités, VIII , vol.381 , pp. 11-19
    • Bretagnolle, J.1
  • 13
    • 0035625342 scopus 로고    scopus 로고
    • The maximum maximum of a martingale constrained by an intermediate law
    • MR1826407
    • H. Brown, D. Hobson, and L. C. G. Rogers. The maximum maximum of a martingale constrained by an intermediate law. Probab. Theory Related Fields, 119(4):558-578, 2001. MR1826407
    • (2001) Probab. Theory Related Fields , vol.119 , Issue.4 , pp. 558-578
    • Brown, H.1    Hobson, D.2    Rogers, L.C.G.3
  • 14
    • 84890672994 scopus 로고    scopus 로고
    • Une preuve standard du principe d'invariance de Stoll
    • of Lecture Notes in Math., Springer, Berlin, MR1478720
    • B. Cadre. Une preuve standard du principe d'invariance de Stoll. In Séminaire de Probabilités, XXXI, volume 1655 of Lecture Notes in Math., pages 85-102. Springer, Berlin, 1997. MR1478720
    • (1997) In Séminaire de Probabilités, XXXI , vol.1655 , pp. 85-102
    • Cadre, B.1
  • 15
    • 0010966220 scopus 로고
    • A metric characterization of the set of functions whose conjugate functions are integrable
    • MR410232
    • O. D. Cereteli. A metric characterization of the set of functions whose conjugate functions are integrable. Sakharth. SSR Mecn. Akad. Moambe, 81(2):281-283, 1976. MR410232
    • (1976) Sakharth. SSR Mecn. Akad. Moambe , vol.81 , Issue.2 , pp. 281-283
    • Cereteli, O.D.1
  • 17
    • 47249108335 scopus 로고
    • Potential processes
    • MR501374
    • R. V. Chacon. Potential processes. Trans. Amer. Math. Soc., 226:39-58, 1977. MR501374
    • (1977) Trans. Amer. Math. Soc. , vol.226 , pp. 39-58
    • Chacon, R.V.1
  • 19
    • 0000431566 scopus 로고
    • One-dimensional potential embedding
    • Lecture Notes in Math., Springer, Berlin, MR445598
    • R. V. Chacon and J. B. Walsh. One-dimensional potential embedding. In Séminaire de Probabilités, X, pages 19-23. Lecture Notes in Math., Vol. 511. Springer, Berlin, 1976. MR445598
    • (1976) In Séminaire de Probabilités, X , vol.511 , pp. 19-23
    • Chacon, R.V.1    Walsh, J.B.2
  • 20
    • 0042107489 scopus 로고    scopus 로고
    • Rates of convergence in the functional CLT for martingales
    • MR1679980
    • B. Courbot. Rates of convergence in the functional CLT for martingales. C. R. Acad. Sci. Paris Sér. I Math., 328(6):509-513, 1999. MR1679980
    • (1999) C. R. Acad. Sci. Paris Sér. I Math. , vol.3287 , Issue.6 , pp. 509-513
    • Courbot, B.1
  • 23
    • 1642542012 scopus 로고    scopus 로고
    • An optimal Skorokhod embedding for diffusions
    • MR2049567
    • A. Cox and D. Hobson. An optimal Skorokhod embedding for diffusions. Stochastic Process. Appl., 111(1):17-39, 2004. MR2049567
    • (2004) Stochastic Process. Appl. , vol.111 , Issue.1 , pp. 17-39
    • Cox, A.1    Hobson, D.2
  • 25
    • 84963789452 scopus 로고
    • A new method to prove Strassen type laws of invariance principle. I, II. Z. Wahrscheinlichkeitstheorie und Verw
    • MR375411
    • M. Csörgö and P. Révész. A new method to prove Strassen type laws of invariance principle. I, II. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 31:255-269, 1974/75. MR375411
    • (1974) Gebiete , vol.31 , pp. 255-269
    • Csörgö, M.1    Révész, P.2
  • 26
    • 84972583425 scopus 로고
    • On the Lp norms of stochastic integrals and other martingales
    • MR418219
    • B. Davis. On the Lp norms of stochastic integrals and other martingales. Duke Math. J., 43(4):697-704, 1976. MR418219
    • (1976) Duke Math. J. , vol.43 , Issue.4 , pp. 697-704
    • Davis, B.1
  • 27
    • 84968483733 scopus 로고
    • Hardy spaces and rearrangements
    • MR576872
    • B. Davis. Hardy spaces and rearrangements. Trans. Amer. Math. Soc., 261(1):211-233, 1980. MR576872
    • (1980) Trans. Amer. Math. Soc. , vol.261 , Issue.1 , pp. 211-233
    • Davis, B.1
  • 28
    • 0042238398 scopus 로고    scopus 로고
    • Sur l'indépendance d'un temps d'arrêt T et de la position BT d'un mouvement brownien (Bu; u ≥ 0)
    • MR1872465
    • B. De Meyer, B. Roynette, P. Vallois, and M. Yor. Sur l'indépendance d'un temps d'arrêt T et de la position BT d'un mouvement brownien (Bu; u ≥ 0). C. R. Acad. Sci. Paris Sér. I Math., 333(11):1017-1022, 2001. MR1872465
    • (2001) C. R. Acad. Sci. Paris Sér. I Math. , vol.333 , Issue.11 , pp. 1017-1022
    • De Meyer, B.1    Roynette, B.2    Vallois, P.3    Yor, M.4
  • 29
    • 0036994938 scopus 로고    scopus 로고
    • On independent times and positions for Brownian motions
    • MR1954864
    • B. de Meyer, B. Roynette, P. Vallois, and M. Yor. On independent times and positions for Brownian motions. Rev. Mat. Iberoamericana, 18(3):541- 586, 2002. MR1954864
    • (2002) Rev. Mat. Iberoamericana , vol.18 , Issue.3
    • de Meyer, B.1    Roynette, B.2    Vallois, P.3    Yor, M.4
  • 30
    • 0013255002 scopus 로고    scopus 로고
    • Affine random equations and the stable ( 1 2 ) distribution
    • MR1798746
    • C. Donati-Martin, R. Ghomrasni, and M. Yor. Affine random equations and the stable ( 1 2 ) distribution. Studia Sci. Math. Hungar., 36(3-4):387- 405, 2000. MR1798746
    • (2000) Studia Sci. Math. Hungar. , vol.36 , Issue.3-4
    • Donati-Martin, C.1    Ghomrasni, R.2    Yor, M.3
  • 31
    • 0000503150 scopus 로고
    • On a theorem of Skorohod
    • MR234520
    • L. E. Dubins. On a theorem of Skorohod. Ann. Math. Statist., 39:2094- 2097, 1968. MR234520
    • (1968) Ann. Math. Statist. , vol.39
    • Dubins, L.E.1
  • 32
    • 84966232430 scopus 로고
    • On the distribution of maxima of martingales
    • MR494473
    • L. E. Dubins and D. Gilat. On the distribution of maxima of martingales. Proc. Amer. Math. Soc., 68(3):337-338, 1978. MR494473
    • (1978) Proc. Amer. Math. Soc. , vol.68 , Issue.3 , pp. 337-338
    • Dubins, L.E.1    Gilat, D.2
  • 33
    • 4243894658 scopus 로고
    • A sharp inequality for sub-martingales and stopping-times
    • Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987). MR976216
    • L. E. Dubins and G. Schwarz. A sharp inequality for sub-martingales and stopping-times. Astérisque, (157-158):129-145, 1988. Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987). MR976216
    • (1988) Astérisque , vol.157-158 , pp. 129-145
    • Dubins, L.E.1    Schwarz, G.2
  • 34
    • 0001744448 scopus 로고
    • Optimal stopping rules and maximal inequalities for Bessel processes
    • MR1317981
    • L. E. Dubins, L. A. Shepp, and A. N. Shiryaev. Optimal stopping rules and maximal inequalities for Bessel processes. Teor. Veroyatnost. i Primenen., 38(2):288-330, 1993. MR1317981
    • (1993) Teor. Veroyatnost. i Primenen. , vol.38 , Issue.2 , pp. 288-330
    • Dubins, L.E.1    Shepp, L.A.2    Shiryaev, A.N.3
  • 35
    • 0002431534 scopus 로고
    • Extensions of results of Komlós, Major, and Tusnády to the multivariate case
    • MR996984
    • U. Einmahl. Extensions of results of Komlós, Major, and Tusnády to the multivariate case. J. Multivariate Anal., 28(1):20-68, 1989. MR996984
    • (1989) J. Multivariate Anal. , vol.28 , Issue.1 , pp. 20-68
    • Einmahl, U.1
  • 36
    • 0013211847 scopus 로고
    • On Skorohod embedding in n-dimensional Brownian motion by means of natural stopping times
    • of Lecture Notes in Math., Springer, Berlin, MR580142
    • N. Falkner. On Skorohod embedding in n-dimensional Brownian motion by means of natural stopping times. In Séminaire de Probabilitées, XIV, volume 784 of Lecture Notes in Math., pages 357-391. Springer, Berlin, 1980. MR580142
    • (1980) In Séminaire de Probabilitées, XIV , Issue.784 , pp. 357-391
    • Falkner, N.1
  • 37
    • 0013212752 scopus 로고
    • Stopping distributions for right processes
    • MR1113221
    • N. Falkner and P. J. Fitzsimmons. Stopping distributions for right processes. Probab. Theory Related Fields, 89(3):301-318, 1991. MR1113221
    • (1991) Probab. Theory Related Fields , vol.89 , Issue.3 , pp. 301-318
    • Falkner, N.1    Fitzsimmons, P.J.2
  • 38
    • 27144552324 scopus 로고
    • Penetration times and Skorohod stopping
    • of Lecture Notes in Math., Springer, Berlin, MR960524
    • P. J. Fitzsimmons. Penetration times and Skorohod stopping. In Séminaire de Probabilités, XXII, volume 1321 of Lecture Notes in Math., pages 166-174. Springer, Berlin, 1988. MR960524
    • (1988) In Séminaire de Probabilités, XXII , vol.1321 , pp. 166-174
    • Fitzsimmons, P.J.1
  • 39
    • 84890782427 scopus 로고
    • Corrections to: \Penetration times and Skorohod stopping" (see [38])
    • of Lecture Notes in Math., Springer, Berlin, MR1022939
    • P. J. Fitzsimmons. Corrections to: \Penetration times and Skorohod stopping" (see [38]). In Séminaire de Probabilités, XXIII, volume 1372 of Lecture Notes in Math., page 583. Springer, Berlin, 1989. MR1022939
    • (1989) In Séminaire de Probabilités, XXIII , vol.1372 , pp. 583
    • Fitzsimmons, P.J.1
  • 40
    • 0007211734 scopus 로고
    • Skorokhod embedding by randomized hitting times
    • (Vancouver, BC, 1990), of Progr. Probab., Birkhäuser Boston, Boston, MA, 1991. MR1118443
    • P. J. Fitzsimmons. Skorokhod embedding by randomized hitting times. In Seminar on Stochastic Processes, 1990 (Vancouver, BC, 1990), volume 24 of Progr. Probab., pages 183-191. Birkhäuser Boston, Boston, MA, 1991. MR1118443
    • (1990) In Seminar on Stochastic Processes , vol.24 , pp. 83-191
    • Fitzsimmons, P.J.1
  • 41
    • 0011975680 scopus 로고    scopus 로고
    • Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process
    • MR1670526
    • P. J. Fitzsimmons and J. Pitman. Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process. Stochastic Process. Appl., 79(1):117-134, 1999. MR1670526
    • (1999) Stochastic Process. Appl. , vol.79 , Issue.1 , pp. 117-134
    • Fitzsimmons, P.J.1    Pitman, J.2
  • 43
    • 0003827228 scopus 로고
    • Holden-Day, San Francisco, Calif., MR292176
    • D. Freedman. Markov chains. Holden-Day, San Francisco, Calif., 1971. MR292176
    • (1971) Markov chains
    • Freedman, D.1
  • 45
    • 1042285606 scopus 로고    scopus 로고
    • A survey and some generalizations of Bessel processes
    • MR1997032
    • A. Göing-Jaeschke and M. Yor. A survey and some generalizations of Bessel processes. Bernoulli, 9(2):313-349, 2003. MR1997032
    • (2003) Bernoulli , vol.9 , Issue.2 , pp. 313-349
    • Göing-Jaeschke, A.1    Yor, M.2
  • 46
    • 0043125017 scopus 로고    scopus 로고
    • Embedding in Brownian motion with drift and the Azéma-Yor construction
    • MR1731025
    • P. Grandits and N. Falkner. Embedding in Brownian motion with drift and the Azéma-Yor construction. Stochastic Process. Appl., 85(2):249- 254, 2000. MR1731025
    • (2000) Stochastic Process. Appl. , vol.85 , Issue.2
    • Grandits, P.1    Falkner, N.2
  • 47
    • 53349115155 scopus 로고    scopus 로고
    • Information and option pricings
    • MR1810015
    • X. Guo. Information and option pricings. Quant. Finance, 1(1):38-44, 2001. MR1810015
    • (2001) Quant. Finance , vol.1 , Issue.1 , pp. 38-44
    • Guo, X.1
  • 48
    • 0033148230 scopus 로고    scopus 로고
    • Weighted approximations to continuous time martingales with applications
    • MR1707654
    • E. Haeusler and D. M. Mason. Weighted approximations to continuous time martingales with applications. Scand. J. Statist., 26(2):281-295, 1999. MR1707654
    • (1999) Scand. J. Statist. , vol.26 , Issue.2 , pp. 281-295
    • Haeusler, E.1    Mason, D.M.2
  • 49
    • 48849104923 scopus 로고
    • Technical Report 33, Stanford Univ., Dept. of Stat.
    • W. Hall. On the Skorokhod embedding theorem. Technical Report 33, Stanford Univ., Dept. of Stat., 1968.
    • (1968) On the Skorokhod embedding theorem
    • Hall, W.1
  • 50
    • 44049087905 scopus 로고
    • Embedding submartingales in Wiener processes with drift, with applications to sequential analysis
    • MR256459
    • W. J. Hall. Embedding submartingales in Wiener processes with drift, with applications to sequential analysis. J. Appl. Probability, 6:612-632, 1969. MR256459
    • (1969) J. Appl. Probability , vol.6 , pp. 612-632
    • Hall, W.J.1
  • 51
    • 0142087745 scopus 로고    scopus 로고
    • Law of the iterated logarithm for oscillating random walks conditioned to stay non-negative
    • MR2019057
    • B. Hambly, G. Kersting, and A. Kyprianou. Law of the iterated logarithm for oscillating random walks conditioned to stay non-negative. Stochastic Process. Appl., 108:327-343, 2002. MR2019057
    • (2002) Stochastic Process. Appl. , vol.108 , pp. 327-343
    • Hambly, B.1    Kersting, G.2    Kyprianou, A.3
  • 52
    • 84968511170 scopus 로고
    • First passage and recurrence distributions
    • MR52057
    • T. E. Harris. First passage and recurrence distributions. Trans. Amer. Math. Soc., 73:471-486, 1952. MR52057
    • (1952) Trans. Amer. Math. Soc. , vol.73 , pp. 471-486
    • Harris, T.E.1
  • 53
    • 0040851041 scopus 로고
    • Skorokhod stopping via potential theory
    • Lecture Notes in Math., Springer, Berlin, MR368185
    • D. Heath. Skorokhod stopping via potential theory. In Séminaire de Probabilit és, VIII, pages 150-154. Lecture Notes in Math., Vol. 381. Springer, Berlin, 1974. MR368185
    • (1974) In Séminaire de Probabilit és, VIII , vol.381 , pp. 150-154
    • Heath, D.1
  • 55
    • 0036018196 scopus 로고    scopus 로고
    • The minimum maximum of a continuous martingale with given initial and terminal laws
    • MR1906424
    • D. G. Hobson and J. L. Pedersen. The minimum maximum of a continuous martingale with given initial and terminal laws. Ann. Probab., 30(2):978- 999, 2002. MR1906424
    • (2002) Ann. Probab. , vol.30 , Issue.2
    • Hobson, D.G.1    Pedersen, J.L.2
  • 56
    • 69149086684 scopus 로고
    • Note on the central limit theorem for stationary processes
    • of Lecture Notes in Math., Springer, Berlin, MR770417
    • P. J. Holewijn and I. Meilijson. Note on the central limit theorem for stationary processes. In Séminaire de Probabilités, XVII, volume 986 of Lecture Notes in Math., pages 240-242. Springer, Berlin, 1983. MR770417
    • (1983) Séminaire de Probabilités, XVII , vol.986 , pp. 240-242
    • Holewijn, P.J.1    Meilijson, I.2
  • 57
    • 17444427227 scopus 로고    scopus 로고
    • The logarithmic average of Sinai's walk in random environment
    • Endre Csáki 65. MR1812804
    • Y. Hu. The logarithmic average of Sinai's walk in random environment. Period. Math. Hungar., 41(1-2):175-185, 2000. Endre Csáki 65. MR1812804
    • (2000) Period. Math. Hungar. , vol.41 , Issue.1-2 , pp. 175-185
    • Hu, Y.1
  • 58
    • 0001720971 scopus 로고
    • Doob's inequalities revisited: a maximal H1-embedding
    • MR958505
    • S. D. Jacka. Doob's inequalities revisited: a maximal H1-embedding. Stochastic Process. Appl., 29(2):281-290, 1988. MR958505
    • (1988) Stochastic Process. Appl. , vol.29 , Issue.2 , pp. 281-290
    • Jacka, S.D.1
  • 59
    • 0039477093 scopus 로고
    • Optimal stopping and best constants for Doob-like inequalities
    • MR1127729
    • S. D. Jacka. Optimal stopping and best constants for Doob-like inequalities. I. The case p = 1. Ann. Probab., 19(4):1798-1821, 1991. MR1127729
    • (1991) I. The case p = 1. Ann. Probab. , vol.19 , Issue.4 , pp. 1798-1821
    • Jacka, S.D.1
  • 60
    • 0040051739 scopus 로고
    • Sur les distributions de certaines fonctionnelles du mouvement brownien
    • of Lecture Notes in Math., Springer, Berlin, MR622565
    • T. Jeulin and M. Yor. Sur les distributions de certaines fonctionnelles du mouvement brownien. In Séminaire de Probabilités, XV, volume 850 of Lecture Notes in Math., pages 210-226. Springer, Berlin, 1981. MR622565
    • (1981) Séminaire de Probabilités, XV, , vol.850 , pp. 210-226
    • Jeulin, T.1    Yor, M.2
  • 61
    • 0000097376 scopus 로고
    • Martingales with given maxima and terminal distributions
    • MR1045372
    • R. P. Kertz and U. Rösler. Martingales with given maxima and terminal distributions. Israel J. Math., 69(2):173-192, 1990. MR1045372
    • (1990) Israel J. Math. , vol.69 , Issue.2 , pp. 173-192
    • Kertz, R.P.1    Rösler, U.2
  • 62
    • 25444432373 scopus 로고
    • An embedding of compensated compound Poisson processes with applications to local times
    • MR1207230
    • D. Khoshnevisan. An embedding of compensated compound Poisson processes with applications to local times. Ann. Probab., 21(1):340-361, 1993. MR1207230
    • (1993) Ann. Probab. , vol.21 , Issue.1 , pp. 340-361
    • Khoshnevisan, D.1
  • 63
    • 0000446609 scopus 로고
    • On the deviations in the Skorokhod-Strassen approximation scheme
    • MR256461
    • J. Kiefer. On the deviations in the Skorokhod-Strassen approximation scheme. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 13:321-332, 1969. MR256461
    • (1969) Z. Wahrscheinlichkeitstheorie und Verw. Gebiete , vol.13 , pp. 321-332
    • Kiefer, J.1
  • 64
    • 0003050745 scopus 로고
    • Skorohod embedding of multivariate rv's, and the sample df
    • MR341636
    • J. Kiefer. Skorohod embedding of multivariate rv's, and the sample df. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 24:1-35, 1972. MR341636
    • (1972) Z. Wahrscheinlichkeitstheorie und Verw. Gebiete , vol.24 , pp. 1-35
    • Kiefer, J.1
  • 65
    • 84968484397 scopus 로고
    • On the random walk and Brownian motion
    • MR139211
    • F. B. Knight. On the random walk and Brownian motion. Trans. Amer. Math. Soc., 103:218-228, 1962. MR139211
    • (1962) Trans. Amer. Math. Soc. , vol.103 , pp. 218-228
    • Knight, F.B.1
  • 66
    • 84968484961 scopus 로고
    • Random walks and a sojourn density process of Brownian motion
    • MR154337
    • F. B. Knight. Random walks and a sojourn density process of Brownian motion. Trans. Amer. Math. Soc., 109:56-86, 1963. MR154337
    • (1963) Trans. Amer. Math. Soc. , vol.109 , pp. 56-86
    • Knight, F.B.1
  • 67
    • 0031588896 scopus 로고    scopus 로고
    • Approximation of stopped Brownian local time by diadic crossing chains
    • MR1440401
    • F. B. Knight. Approximation of stopped Brownian local time by diadic crossing chains. Stochastic Process. Appl., 66(2):253-270, 1997. MR1440401
    • (1997) Stochastic Process. Appl. , vol.66 , Issue.2 , pp. 253-270
    • Knight, F.B.1
  • 69
    • 84890593578 scopus 로고
    • The moment of crossing of diffusion processes over boundaries that depend on time
    • MR290462
    • V. A. Lebedev. The moment of crossing of diffusion processes over boundaries that depend on time. Teor. Verojatnost. i Primenen., 16:551-556, 1971. MR290462
    • (1971) Teor. Verojatnost. i Primenen. , vol.16 , pp. 551-556
    • Lebedev, V.A.1
  • 70
    • 34250500031 scopus 로고
    • Stopping times on Brownian motion: Some properties of Root's construction
    • MR292170
    • R. M. Loynes. Stopping times on Brownian motion: Some properties of Root's construction. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 16:211-218, 1970. MR292170
    • (1970) Z. Wahrscheinlichkeitstheorie und Verw. Gebiete , vol.16 , pp. 211-218
    • Loynes, R.M.1
  • 71
    • 12144274928 scopus 로고    scopus 로고
    • Making Markov martingales meet marginals: with explicit constructions
    • MR1914701
    • D. B. Madan and M. Yor. Making Markov martingales meet marginals: with explicit constructions. Bernoulli, 8(4):509-536, 2002. MR1914701
    • (2002) Bernoulli , vol.8 , Issue.4 , pp. 509-536
    • Madan, D.B.1    Yor, M.2
  • 72
    • 84890784856 scopus 로고
    • There exists no ultimate solution to Skorokhod's problem
    • of Lecture Notes in Math., Springer, Berlin, MR658701
    • I. Meilijson. There exists no ultimate solution to Skorokhod's problem. In Séminaire de Probabilités, XVI, volume 920 of Lecture Notes in Math., pages 392-399. Springer, Berlin, 1982. MR658701
    • (1982) Séminaire de Probabilités, XVI , vol.920 , pp. 392-399
    • Meilijson, I.1
  • 73
    • 0009858445 scopus 로고
    • On the Azéma-Yor stopping time
    • of Lecture Notes in Math., Springer, Berlin, MR770415
    • I. Meilijson. On the Azéma-Yor stopping time. In Séminaire de Probabilit és, XVII, volume 986 of Lecture Notes in Math., pages 225-226. Springer, Berlin, 1983. MR770415
    • (1983) Séminaire de Probabilit és, XVII , vol.986 , pp. 225-226
    • Meilijson, I.1
  • 75
    • 33747266821 scopus 로고    scopus 로고
    • The time to a given drawdown in Brownian motion
    • of Lecture Notes in Math., Springer, Berlin, MR2053044
    • I. Meilijson. The time to a given drawdown in Brownian motion. In Séminaire de Probabilités, XXXVII, volume 1832 of Lecture Notes in Math., pages 94-108. Springer, Berlin, 2003. MR2053044
    • (2003) Séminaire de Probabilités, XXXVII, , vol.1832 , pp. 94-108
    • Meilijson, I.1
  • 76
    • 84890584163 scopus 로고
    • Sur un article de Dubins
    • Lecture Notes in Math., Springer, Berlin, MR375456
    • P. A. Meyer. Sur un article de Dubins. In Séminaire de Probabilités, V, pages 170-176. Lecture Notes in Math., Vol. 191. Springer, Berlin, 1971. MR375456
    • (1971) Séminaire de Probabilités, V , vol.191 , pp. 170-176
    • Meyer, P.A.1
  • 77
    • 0010191322 scopus 로고
    • Le schéma de remplissage en temps continu, d'après H. Rost
    • Lecture Notes in Math., Springer, Berlin, MR402946
    • P. A. Meyer. Le schéma de remplissage en temps continu, d'après H. Rost. In Séminaire de Probabilités, VI, pages 130-150. Lecture Notes in Math., Vol. 258. Springer, Berlin, 1972. MR402946
    • (1972) Séminaire de Probabilités, VI , vol.258 , pp. 130-150
    • Meyer, P.A.1
  • 78
    • 0040536301 scopus 로고
    • On embedding right continuous martingales in Brownian motion
    • MR343354
    • I. Monroe. On embedding right continuous martingales in Brownian motion. Ann. Math. Statist., 43:1293-1311, 1972. MR343354
    • (1972) Ann. Math. Statist. , vol.43 , pp. 1293-1311
    • Monroe, I.1
  • 79
    • 84871254071 scopus 로고
    • Using additive functionals to embed preassigned distributions in symmetric stable processes
    • MR298768
    • I. Monroe. Using additive functionals to embed preassigned distributions in symmetric stable processes. Trans. Amer. Math. Soc., 163:131-146, 1972. MR298768
    • (1972) Trans. Amer. Math. Soc. , vol.163 , pp. 131-146
    • Monroe, I.1
  • 80
    • 0002871754 scopus 로고
    • Processes that can be embedded in Brownian motion
    • MR455113
    • I. Monroe. Processes that can be embedded in Brownian motion. Ann. Probability, 6(1):42-56, 1978. MR455113
    • (1978) Ann. Probability , vol.6 , Issue.1 , pp. 42-56
    • Monroe, I.1
  • 81
    • 0004239351 scopus 로고    scopus 로고
    • North-Holland Publishing Co., Amsterdam, revised edition, 1975. Translated from the French by T. P. Speed, North-Holland Mathematical Library, MR402915
    • J. Neveu. Discrete-parameter martingales. North-Holland Publishing Co., Amsterdam, revised edition, 1975. Translated from the French by T. P. Speed, North-Holland Mathematical Library, Vol. 10. MR402915
    • Discrete-parameter martingales , vol.10
    • Neveu, J.1
  • 82
    • 0009043167 scopus 로고
    • The stopping times of a Wiener process
    • MR315798
    • A. A. Novikov. The stopping times of a Wiener process. Teor. Verojatnost. i Primenen., 16:458-465, 1971. MR315798
    • (1971) Teor. Verojatnost. i Primenen. , vol.16 , pp. 458-465
    • Novikov, A.A.1
  • 84
    • 0742289208 scopus 로고    scopus 로고
    • An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale
    • MR2052138
    • J. Oblój and M. Yor. An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale. Stochastic Process. Appl., 110(1):83-110, 2004. MR2052138
    • (2004) Stochastic Process. Appl. , vol.110 , Issue.1 , pp. 83-110
    • Oblój, J.1    Yor, M.2
  • 87
    • 34248196220 scopus 로고    scopus 로고
    • Optimal prediction of the ultimate maximum of Brownian motion
    • MR1994906
    • J. L. Pedersen. Optimal prediction of the ultimate maximum of Brownian motion. Stoch. Stoch. Rep., 75(4):205-219, 2003. MR1994906
    • (2003) Stoch. Stoch. Rep. , vol.75 , Issue.4 , pp. 205-219
    • Pedersen, J.L.1
  • 88
    • 21844435511 scopus 로고    scopus 로고
    • Computing the expectation of the Azéma- Yor stopping times
    • MR1614599
    • J. L. Pedersen and G. Peškir. Computing the expectation of the Azéma- Yor stopping times. Ann. Inst. H. Poincaré Probab. Statist., 34(2):265- 276, 1998. MR1614599
    • (1998) Ann. Inst. H. Poincaré Probab. Statist. , vol.34 , Issue.2
    • Pedersen, J.L.1    Peškir, G.2
  • 89
    • 0041334092 scopus 로고    scopus 로고
    • The Azéma-Yor embedding in non-singular diffusions
    • MR1865760
    • J. L. Pedersen and G. Peškir. The Azéma-Yor embedding in non-singular diffusions. Stochastic Process. Appl., 96(2):305-312, 2001. MR1865760
    • (2001) Stochastic Process. Appl. , vol.96 , Issue.2 , pp. 305-312
    • Pedersen, J.L.1    Peškir, G.2
  • 90
    • 0010264885 scopus 로고
    • The Cereteli-Davis solution to the H1-embedding problem and an optimal embedding in Brownian motion
    • (Gainesville, Fla., 1985), volume 12 of Progr. Probab. Statist., Birkhäuser Boston, Boston, MA, 1986. MR896743
    • E. Perkins. The Cereteli-Davis solution to the H1-embedding problem and an optimal embedding in Brownian motion. In Seminar on stochastic processes, 1985 (Gainesville, Fla., 1985), volume 12 of Progr. Probab. Statist., pages 172-223. Birkhäuser Boston, Boston, MA, 1986. MR896743
    • (1985) Seminar on stochastic processes , pp. 172-223
    • Perkins, E.1
  • 91
    • 0032237702 scopus 로고    scopus 로고
    • Optimal stopping of the maximum process: the maximality principle
    • MR1675047
    • G. Peskir. Optimal stopping of the maximum process: the maximality principle. Ann. Probab., 26(4):1614-1640, 1998. MR1675047
    • (1998) Ann. Probab. , vol.26 , Issue.4 , pp. 1614-1640
    • Peskir, G.1
  • 92
    • 0041595465 scopus 로고    scopus 로고
    • Designing options given the risk: the optimal Skorokhodembedding problem
    • MR1680505
    • G. Peskir. Designing options given the risk: the optimal Skorokhodembedding problem. Stochastic Process. Appl., 81(1):25-38, 1999. MR1680505
    • (1999) Stochastic Process. Appl. , vol.81 , Issue.1 , pp. 25-38
    • Peskir, G.1
  • 93
    • 44049097768 scopus 로고    scopus 로고
    • The Azéma-Yor embedding in Brownian motion with drift
    • (Seattle, WA, 1999), of Progr. Probab., Birkhäuser Boston, Boston, MA, MR1857324
    • G. Peskir. The Azéma-Yor embedding in Brownian motion with drift. In High dimensional probability, II (Seattle, WA, 1999), volume 47 of Progr. Probab., pages 207-221. Birkhäuser Boston, Boston, MA, 2000. MR1857324
    • (2000) High dimensional probability, II , vol.47 , pp. 207-221
    • Peskir, G.1
  • 95
    • 0742266308 scopus 로고
    • Le problème de Skorokhod: une remarque sur la démonstration d'Azéma-Yor
    • (Paris, 1978/1979) (French), of Lecture Notes in Math., Springer, Berlin, MR580143
    • M. Pierre. Le problème de Skorokhod: une remarque sur la démonstration d'Azéma-Yor. In Séminaire de Probabilités, XIV (Paris, 1978/1979) (French), volume 784 of Lecture Notes in Math., pages 392-396. Springer, Berlin, 1980. MR580143
    • (1980) Séminaire de Probabilités, XIV , vol.784 , pp. 392-396
    • Pierre, M.1
  • 96
    • 0041117282 scopus 로고
    • An identity for stopping times of a Markov process
    • (papers in honour of Edwin J. G. Pitman), North-Holland, Amsterdam, MR431384
    • J. W. Pitman. An identity for stopping times of a Markov process. In Studies in probability and statistics (papers in honour of Edwin J. G. Pitman), pages 41-57. North-Holland, Amsterdam, 1976. MR431384
    • (1976) Studies in probability and statistics , pp. 41-57
    • Pitman, J.W.1
  • 97
    • 0010899493 scopus 로고
    • Occupation measures for Markov chains
    • MR433600
    • J. W. Pitman. Occupation measures for Markov chains. Advances in Appl. Probability, 9(1):69-86, 1977. MR433600
    • (1977) Advances in Appl. Probability , vol.9 , Issue.1 , pp. 69-86
    • Pitman, J.W.1
  • 98
    • 0001376031 scopus 로고
    • Mesures associées aux fonctionnelles additives de Markov
    • MR279890
    • D. Revuz. Mesures associées aux fonctionnelles additives de Markov. I. Trans. Amer. Math. Soc., 148:501-531, 1970. MR279890
    • (1970) I. Trans. Amer. Math. Soc. , vol.148 , pp. 501-531
    • Revuz, D.1
  • 99
    • 0003543379 scopus 로고    scopus 로고
    • of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, third edition, MR1725357
    • D. Revuz and M. Yor. Continuous martingales and Brownian motion, volume 293 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, third edition, 1999. MR1725357
    • (1999) Continuous martingales and Brownian motion , vol.293
    • Revuz, D.1    Yor, M.2
  • 100
    • 0039147560 scopus 로고
    • Boundary crossing probabilities for the Wiener process and sample sums
    • MR277059
    • H. Robbins and D. Siegmund. Boundary crossing probabilities for the Wiener process and sample sums. Ann. Math. Statist., 41:1410-1429, 1970. MR277059
    • (1970) Ann. Math. Statist. , vol.41 , pp. 1410-1429
    • Robbins, H.1    Siegmund, D.2
  • 101
    • 0010265665 scopus 로고
    • Williams' characterisation of the Brownian excursion law: proof and applications
    • of Lecture Notes in Math., Springer, Berlin, MR622566
    • L. C. G. Rogers. Williams' characterisation of the Brownian excursion law: proof and applications. In Séminaire de Probabilités, XV, volume 850 of Lecture Notes in Math., pages 227-250. Springer, Berlin, 1981. MR622566
    • (1981) Séminaire de Probabilités, XV , vol.850 , pp. 227-250
    • Rogers, L.C.G.1
  • 102
    • 21144483218 scopus 로고
    • The joint law of the maximum and terminal value of a martingale
    • MR1217446
    • L. C. G. Rogers. The joint law of the maximum and terminal value of a martingale. Probab. Theory Related Fields, 95(4):451-466, 1993. MR1217446
    • (1993) Probab. Theory Related Fields , vol.95 , Issue.4 , pp. 451-466
    • Rogers, L.C.G.1
  • 103
    • 0013258412 scopus 로고
    • The existence of certain stopping times on Brownian motion
    • MR238394
    • D. H. Root. The existence of certain stopping times on Brownian motion. Ann. Math. Statist., 40:715-718, 1969. MR238394
    • (1969) Ann. Math. Statist. , vol.40 , pp. 715-718
    • Root, D.H.1
  • 104
    • 0041543882 scopus 로고
    • Die Stoppverteilungen eines Markoff-Prozesses mit lokalendlichem Potential
    • MR273691
    • H. Rost. Die Stoppverteilungen eines Markoff-Prozesses mit lokalendlichem Potential. Manuscripta Math., 3:321-329, 1970. MR273691
    • (1970) Manuscripta Math. , vol.3 , pp. 321-329
    • Rost, H.1
  • 105
    • 0002688781 scopus 로고
    • The stopping distributions of a Markov Process
    • MR346920
    • H. Rost. The stopping distributions of a Markov Process. Invent. Math., 14:1-16, 1971. MR346920
    • (1971) Invent. Math. , vol.14 , pp. 1-16
    • Rost, H.1
  • 106
    • 0742283667 scopus 로고
    • Skorokhod's theorem for general Markov processes
    • (Tech. Univ. Prague, Prague, 1971; dedicated to the memory of Antonín Špaček), Academia, Prague, MR356248
    • H. Rost. Skorokhod's theorem for general Markov processes. In Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Tech. Univ. Prague, Prague, 1971; dedicated to the memory of Antonín Špaček), pages 755-764. Academia, Prague, 1973. MR356248
    • (1973) Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes , pp. 755-764
    • Rost, H.1
  • 107
    • 33645965529 scopus 로고
    • Skorokhod stopping times of minimal variance
    • Lecture Notes in Math., Springer, Berlin, MR445600
    • H. Rost. Skorokhod stopping times of minimal variance. In Séminaire de Probabilités, X, pages 194-208. Lecture Notes in Math., Vol. 511. Springer, Berlin, 1976. MR445600
    • (1976) Séminaire de Probabilités, X , vol.511 , pp. 194-208
    • Rost, H.1
  • 108
    • 0013208978 scopus 로고    scopus 로고
    • A solution to Skorokhod's embedding for linear Brownian motion and its local time
    • MR1909150
    • B. Roynette, P. Vallois, and M. Yor. A solution to Skorokhod's embedding for linear Brownian motion and its local time. Studia Sci. Math. Hungar., 39(1-2):97-127, 2002. MR1909150
    • (2002) Studia Sci. Math. Hungar. , vol.39 , Issue.1-2 , pp. 97-127
    • Roynette, B.1    Vallois, P.2    Yor, M.3
  • 110
    • 84879931405 scopus 로고
    • The Skorokhod representation
    • Papers arising from a Conference on Stochastic Differential Equations (Univ. Alberta, Edmonton, Alta., 1972). MR356161
    • S. Sawyer. The Skorokhod representation. Rocky Mountain J. Math., 4:579-596, 1974. Papers arising from a Conference on Stochastic Differential Equations (Univ. Alberta, Edmonton, Alta., 1972). MR356161
    • (1974) Rocky Mountain J. Math. , vol.4 , pp. 579-596
    • Sawyer, S.1
  • 111
    • 84971185419 scopus 로고
    • On the embedding of processes in Brownian motion and the law of the iterated logarithm for reverse martingales
    • MR715321
    • D. J. Scott and R. M. Huggins. On the embedding of processes in Brownian motion and the law of the iterated logarithm for reverse martingales. Bull. Austral. Math. Soc., 27(3):443-459, 1983. MR715321
    • (1983) Bull. Austral. Math. Soc. , vol.27 , Issue.3 , pp. 443-459
    • Scott, D.J.1    Huggins, R.M.2
  • 113
    • 0001599563 scopus 로고
    • A first passage problem for the Wiener process
    • MR217879
    • L. A. Shepp. A first passage problem for the Wiener process. Ann. Math. Statist., 38:1912-1914, 1967. MR217879
    • (1967) Ann. Math. Statist. , vol.38 , pp. 1912-1914
    • Shepp, L.A.1
  • 114
    • 0003907717 scopus 로고
    • (Stokhasticheskie differentsialnye uravneniya i predelnye teoremy dlya protsessov Markova). Izdat. Kiev. Univ., Kiev, MR185619
    • A. V. Skorohod. Issledovaniya po teorii sluchainykh protsessov (Stokhasticheskie differentsialnye uravneniya i predelnye teoremy dlya protsessov Markova). Izdat. Kiev. Univ., Kiev, 1961. MR185619
    • (1961) Issledovaniya po teorii sluchainykh protsessov
    • Skorohod, A.V.1
  • 116
    • 0000571608 scopus 로고
    • Almost sure behavior of sums of independent random variables and martingales
    • (Berkeley, Calif., 1965/66), pages, Contributions to Probability Theory, Part 1, Univ. California Press, Berkeley, Calif., MR214118
    • V. Strassen. Almost sure behavior of sums of independent random variables and martingales. In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), pages Vol. II: Contributions to Probability Theory, Part 1, pp. 315-343. Univ. California Press, Berkeley, Calif., 1967. MR214118
    • (1967) Proc. Fifth Berkeley Sympos. Math. Statist. and Probability , vol.2 , pp. 315-343
    • Strassen, V.1
  • 117
    • 28644432796 scopus 로고    scopus 로고
    • of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, MR1980149
    • D. W. Stroock. Markov processes from K. Itô's perspective, volume 155 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 2003. MR1980149
    • (2003) Markov processes from K. Itô's perspective , vol.155
    • Stroock, D.W.1
  • 118
    • 4043160432 scopus 로고
    • Le problème de Skorokhod sur R: une approche avec le temps local
    • of Lecture Notes in Math., Springer, Berlin, MR770416
    • P. Vallois. Le problème de Skorokhod sur R: une approche avec le temps local. In Séminaire de Probabilités, XVII, volume 986 of Lecture Notes in Math., pages 227-239. Springer, Berlin, 1983. MR770416
    • (1983) Séminaire de Probabilités, XVII , vol.986 , pp. 227-239
    • Vallois, P.1
  • 119
    • 84890649785 scopus 로고
    • On the joint distribution of the supremum and terminal value of a uniformly integrable martingale
    • (Friedrichroda, 1992), of Stochastics Monogr., Gordon and Breach, Montreux, MR1268251
    • P. Vallois. On the joint distribution of the supremum and terminal value of a uniformly integrable martingale. In Stochastic processes and optimal control (Friedrichroda, 1992), volume 7 of Stochastics Monogr., pages 183- 199. Gordon and Breach, Montreux, 1993. MR1268251
    • (1993) Stochastic processes and optimal control , vol.7
    • Vallois, P.1
  • 120
    • 84963044007 scopus 로고
    • Sur la loi du maximum et du temps local d'une martingale continue uniformement intégrable
    • MR1281971
    • P. Vallois. Sur la loi du maximum et du temps local d'une martingale continue uniformement intégrable. Proc. London Math. Soc. (3), 69(2):399- 427, 1994. MR1281971
    • (1994) Proc. London Math. Soc. (3) , vol.69 , Issue.2
    • Vallois, P.1
  • 121
    • 0043152134 scopus 로고
    • Ultimateness and the Azéma-Yor stopping time
    • of Lecture Notes in Math., Springer, Berlin, MR942032
    • D. P. van der Vecht. Ultimateness and the Azéma-Yor stopping time. In Séminaire de Probabilités, XX, 1984/85, volume 1204 of Lecture Notes in Math., pages 375-378. Springer, Berlin, 1986. MR942032
    • (1986) Séminaire de Probabilités, XX, 1984/85 , vol.1204 , pp. 375-378
    • van der Vecht, D.P.1
  • 122
    • 84890772824 scopus 로고    scopus 로고
    • Embedding and the convergence of the binomial and trinomial tree schemes
    • (Toronto, ON, 1999), of Fields Inst. Commun., Amer. Math. Soc., Providence, RI, MR1944748
    • J. B. Walsh and O. D. Walsh. Embedding and the convergence of the binomial and trinomial tree schemes. In Numerical methods and stochastics (Toronto, ON, 1999), volume 34 of Fields Inst. Commun., pages 101-121. Amer. Math. Soc., Providence, RI, 2002. MR1944748
    • (2002) Numerical methods and stochastics , vol.34 , pp. 101-121
    • Walsh, J.B.1    Walsh, O.D.2
  • 124
    • 0004122289 scopus 로고    scopus 로고
    • Part II. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, Some recent martingale problems. MR1442263
    • M. Yor. Some aspects of Brownian motion. Part II. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 1997. Some recent martingale problems. MR1442263
    • (1997) Some aspects of Brownian motion
    • Yor, M.1
  • 125
    • 84890589897 scopus 로고
    • Embedding of semimartingales and Brownian motion
    • MR705730
    • P. Zaremba. Embedding of semimartingales and Brownian motion. Litovsk. Mat. Sb., 23(1):96-100, 1983. MR705730
    • (1983) Litovsk. Mat. Sb. , vol.23 , Issue.1 , pp. 96-100
    • Zaremba, P.1
  • 126
    • 0041543887 scopus 로고
    • Skorokhod problem-elementary proof of the Azéma-Yor formula
    • MR845524
    • P. Zaremba. Skorokhod problem-elementary proof of the Azéma-Yor formula. Probab. Math. Statist., 6(1):11-17, 1985. MR845524
    • (1985) Probab. Math. Statist. , vol.6 , Issue.1 , pp. 11-17
    • Zaremba, P.1
  • 127
    • 84890726798 scopus 로고
    • A new proof of the invariance principle for renewal processes
    • MR1664923
    • H. Zhang and G.-H. Hsu. A new proof of the invariance principle for renewal processes. Sankhyā Ser. A, 56(2):375-378, 1994. MR1664923
    • (1994) Sankhyā Ser. A , vol.56 , Issue.2 , pp. 375-378
    • Zhang, H.1    Hsu, G.-H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.