Stochastic analysis in discrete and continuous settings: With normal martingales

Lecture Notes in Mathematics

Volumn 1982, Issue , 2009, Pages 301-307

  Privault, Nicolas ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

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EID: 85072856432     PISSN: 00758434     EISSN: 16179692     Source Type: Book Series    
DOI: None     Document Type: Chapter

References (153)

1. K. Aase, B. Øksendal, N. Privault, and J. Ubøe. White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance. Finance and Stochastics, 4(4):465–496, 2000.
2. S. Albeverio, A. Daletskii, and E. Lytvynov. De Rham cohomology of configuration spaces with Poisson measure. J. Funct. Anal., 185(1):240–273, 2001.
3. S. Albeverio, Yu. G. Kondratiev, and M. Röckner. Analysis and geometry on configuration spaces. J. Funct. Anal., 154(2):444–500, 1998.
4. C. Ané. Grandes déviations et inégalités fonctionnelles pour des processus de Markov à temps continu sur un graphe. Thèse, Université Paul Sabatier-Toulouse III, 2000.
5. C. Ané, S. Blachère, D. Chafaï, P. Fougères, I. Gentil, F. Malrieu C. Roberto, and G. Scheffer. Sur les inégalités de Sobolev logarithmiques, volume 10 of Panoramas et Synthèses. Société Mathématique de France, Paris, 2000.
6. C. Ané and M. Ledoux. On logarithmic Sobolev inequalities for continuous time random walks on graphs. Probab. Theory Related Fields, 116(4):573–602, 2000.
7. D. Applebaum. Universal malliavin calculus in Fock and Levy-Ito spaces. To appear in Communications on Stochastic Analysis, 2009.
8. S. Attal. Approximating the Fock space with the toy Fock space. In Séminaire de Probabilités, XXXVI, volume 1801 of Lecture Notes in Math., pages 477–491. Springer, Berlin, 2003.
9. S. Attal and M. Émery. Équations de structure pour des martingales vectorielles. In Séminaire de Probabilités, XXVIII, volume 1583 of Lecture Notes in Math., pages 256–278. Springer, Berlin, 1994.
10. S. Attal and M. Émery. Martingales d’Azéma bidimensionnelles. Astérisque, 236:9–21, 1996.
11. D. Barbato. FKG inequality for Brownian motion and stochastic differential equations. Electron. Comm. Probab., 10:7–16 (electronic), 2005.
12. N. Bellamy. Asian options in a market driven by a discontinuous process. Finance, 20(2):69–93, 1999.
13. N. Bellamy. Evaluation et couverture dans un marché dirigé par des processus discontinus. Thèse, Université d’Evry, 1999.
14. M. Berger. A panoramic view of Riemannian geometry. Springer-Verlag, Berlin, 2003.
15. H. Bermin. Essays on Lookback options: a Malliavin calculus approach. PhD thesis, Lund University, 1998.
16. K. Bichteler, J.B. Gravereaux, and J. Jacod. Malliavin Calculus for Processes with Jumps, volume 2 of Stochastics Monographs. Gordon and Breach, 1987.
17. S.G. Bobkov. On the Gross and Talagrand inequalities on the discrete cube. Vestn. Syktyvkar. Univ. Ser. 1 Mat. Mekh. Inform., 1:12–19, 1995.
18. S.G. Bobkov, C. Houdré, and P. Tetali. The subgaussian constant and concentration inequalities. Israel J. Math., 156:255–283, 2006.
19. S.G. Bobkov and M. Ledoux. On modified logarithmic Sobolev inequalities for Bernoulli and Poisson measures. J. Funct. Anal., 156(2):347–365, 1998.
20. N. Bouleau and F. Hirsch. Formes de Dirichlet générales et densité des variables aléatoires réelles sur l’espace de Wiener. J. Funct. Anal., 69:229–259, 1986.
21. J.-C. Breton, C. Houdré, and N. Privault. Dimension free and infinite variance tail estimates on Poisson space. Acta Appl. Math., 95:151–203, 2007.
22. M. Capitaine, E.P. Hsu, and M. Ledoux. Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces. Electron. Comm. Probab., 2:71–81 (electronic), 1997.
23. E. Carlen and E. Pardoux. Differential calculus and integration by parts on Poisson space. In S. Albeverio, Ph. Blanchard, and D. Testard, editors, Stochastics, Algebra and Analysis in Classical and Quantum Dynamics (Marseille, 1988), volume 59 of Math. Appl., pages 63–73. Kluwer Acad. Publ., Dordrecht, 1990.
24. C.S. Chou and P.A. Meyer. Sur la représentation des martingales comme intégrales stochastiques dans les processus ponctuels. In Séminaire de Probabilités, IX, pages 226–236. Lecture Notes in Math., Vol. 465. Springer, Berlin, 1975.
25. Kai Lai Chung. Green, Brown, and probability & Brownian motion on the line. World Scientific Publishing Co. Inc., River Edge, NJ, 2002.
26. R. Cont and P. Tankov. Financial modelling with jump processes. Chapman & Hall/CRC Financial Mathematics Series. Chapman & Hall/CRC, Boca Raton, FL, 2004.
27. A.B. Cruzeiro and P. Malliavin. Renormalized differential geometry on path space: Structural equation, curvature. J. Funct. Anal., 139:119–181, 1996.
28. N. Cutland and S.A. Ng. The Wiener sphere and Wiener measure. Ann. Probab., 21(1):1–13, 1993.
29. P. Dai Pra, A.M. Paganoni, and G. Posta. Entropy inequalities for unbounded spin systems. Ann. Probab., 30(4):1959–1976, 2002.
30. L. Decreusefond and N. Savy. Anticipative calculus with respect to filtered Poisson processes. Ann. Inst. H. Poincaré Probab. Statist., 42(3):343–372, 2006.
31. C. Dellacherie, B. Maisonneuve, and P.A. Meyer. Probabilités et Potentiel, volume 5. Hermann, 1992.
32. A. Dermoune. Differential calculus relative to some point processes. Statistics & Probability Letters, 24:233–242, 1995.
33. A. Dermoune, P. Krée, and L. Wu. Calcul stochastique non adapté par rapport à la mesure de Poisson. In Séminaire de Probabilités XXII, volume 1321 of Lecture Notes in Mathematics, pages 477–484. Springer Verlag, 1988.
34. J. Dieudonné. Éléments d’analyse. Tome II: Chapitres XII à XV. Gauthier-Villars, Éditeur, Paris, 1968.
35. M. Dritschel and Ph. Protter. Complete markets with discontinuous security price. Finance and Stochastics, 3(2):203–214, 1999.
36. R.J. Elliott and A.H. Tsoi. Integration by parts for Poisson processes. J. Multivariate Anal., 44(2):179–190, 1993.
37. M. Émery. On the Azéma martingales. In Séminaire de Probabilités XXIII, volume 1372 of Lecture Notes in Mathematics, pages 66–87. Springer Verlag, 1990.
38. M. Émery. A discrete approach to the chaotic representation property. In Séminaire de Probabilités, XXXV, volume 1755 of Lecture Notes in Math., pages 123–138. Springer, Berlin, 2001.
39. D. Engel. The multiple stochastic integral. Mem. Amer. Math. Soc., 38(265):v+82, 1982.
40. S. Fang. Stochastic anticipative integrals over a Riemannian manifold. J. Funct. Anal., 131:228–253, 1995.
41. S. Fang. Stochastic anticipative calculus on the path space over a compact Riemannian manifold. Journal de Mathématiques Pures et Appliquées, 77(3): 249–282, 1998.
42. S. Fang. Integration by parts formula and logarithmic Sobolev inequality on the path space over loop groups. Ann. Probab., 27(2):664–683, 1999.
43. S. Fang and J. Franchi. Platitude de la structure riemannienne sur le groupe des chemins et identité d’énergie pour les intégrales stochastiques. C. R. Acad. Sci. Paris Sér. I Math., 321(10):1371–1376, 1995.
44. S. Fang and P. Malliavin. Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus. J. Funct. Anal., 118(1):249–274, 1993.
45. H. Föllmer and A. Schied. Stochastic finance, volume 27 of de Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin, 2004.
46. F.Q. Gao and N. Privault. Clark formula and logarithmic Sobolev inequalities for Bernoulli measures. C. R. Math. Acad. Sci. Paris, 336(1):51–56, 2003.
47. F.Q. Gao and J. Quastel. Exponential decay of entropy in the random transposition and Bernoulli-Laplace models. Ann. Appl. Probab., 13(4):1591–1600, 2003.
48. H. Gzyl. An exposé on discrete Wiener chaos expansions. Bol. Asoc. Mat. Venez., XIII(1):3–26, 2006.
49. T. Hida. Analysis of Brownian functionals. Carleton Univ., Ottawa, Ont., 1975. Carleton Mathematical Lecture Notes, No. 13.
50. T. Hida. Brownian Motion. Springer Verlag, 1981.
51. T. Hida, H. H. Kuo, J. Potthoff, and L. Streit. White Noise, An Infinite Dimensional Calculus. Kluwer Acad. Publ., Dordrecht, 1993.
52. F. Hirsch and G. Lacombe. Elements of functional analysis, volume 192 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1999.
53. H. Holden, T. Lindstrøm, B. Øksendal, and J. Ubøe. Discrete Wick calculus and stochastic functional equations. Potential Anal., 1(3):291–306, 1992.
54. H. Holden, T. Lindstrøm, B. Øksendal, and J. Ubøe. Discrete Wick products. In Stochastic analysis and related topics (Oslo, 1992), pages 123–148. Gordon and Breach, Montreux, 1993.
55. C. Houdré. Remarks on deviation inequalities for functions of infinitely divisible random vectors. Ann. Probab., 30(3):1223–1237, 2002.
56. C. Houdré and V. Pérez-Abreu. Covariance identities and inequalities for functionals on Wiener and Poisson spaces. Ann. Probab., 23:400–419, 1995.
57. C. Houdré, V. Pérez-Abreu, and D. Surgailis. Interpolation, correlation identities, and inequalities for infinitely divisible variables. J. Fourier Anal. Appl., 4(6):651–668, 1998.
58. C. Houdré, V. Pérez-Abreu, and A.S. Üstünel. Multiple Wiener-Itô integrals: an introductory survey. In Chaos expansions, multiple Wiener-Itô integrals and their applications (Guanajuato, 1992), Probab. Stochastics Ser., pages 1–33. CRC, Boca Raton, FL, 1994.
59. C. Houdré and N. Privault. Concentration and deviation inequalities in infinite dimensions via covariance representations. Bernoulli, 8(6):697–720, 2002.
60. C. Houdré and N. Privault. A concentration inequality on Riemannian path space. In Stochastic inequalities and applications, volume 56 of Prog. Probab., pages 15–21. Birkhäuser, Basel, 2003.
61. C. Houdré and P. Tetali. Concentration of measure for products of Markov kernels and graph products via functional inequalities. Combin. Probab. Comput., 10(1):1–28, 2001.
62. Y. Hu, A.S. Üstünel, and M. Zakai. Tangent processes on Wiener space. J. Funct. Anal., 192(1):234–270, 2002.
63. Z.Y. Huang and J.A. Yan. Introduction to infinite dimensional stochastic analysis, volume 502 of Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht, 2000.
64. N. Ikeda and S. Watanabe. Stochastic Differential Equations and Diffusion Processes. North-Holland, 1989.
65. P. Imkeller. Malliavin’s Calculus and Applications in Stochastic Control and Finance, volume 1 of IMPAN Lecture Notes. Polish Academy of Sciences, 2008.
66. Y. Ito. Generalized Poisson functionals. Probab. Theory Related Fields, 77:1–28, 1988.
67. J. Jacod and Ph. Protter. Probability essentials. Springer-Verlag, Berlin, 2000.
68. Y.M. Kabanov. On extended stochastic integrals. Theory of Probability and its Applications, XX(4):710–722, 1975.
69. Y. El Khatib. Contributions to the study of discontinuous markets via the Malliavin calculus. Thèse, Université de La Rochelle, 2002.
70. Y. El Khatib and N. Privault. Computations of replicating portfolios in complete markets driven by normal martingales. Applicationes Mathematicae, 30:147–172, 2003.
71. Y. El Khatib and N. Privault. Computations of Greeks in markets with jumps via the Malliavin calculus. Finance and Stochastics, 4(2):161–179, 2004.
72. H.H. Kuo. White Noise Distribution Theory. Probability and Stochastics Series. CRC Press, 1996.
73. S. Kwapień and W. Woyczyński. Random series and stochastic integrals: single and multiple. Probability and its Applications. Birkhäuser Boston Inc., Boston, MA, 1992.
74. D. Lamberton and B. Lapeyre. Introduction to stochastic calculus applied to finance. Chapman & Hall, London, 1996.
75. M. Ledoux. On Talagrand’s deviation inequalities for product measures. ESAIM Probab. Statist., 1:63–87 (electronic), 1995/97.
76. M. Ledoux. Concentration of measure and logarithmic Sobolev inequalities. In Séminaire de Probabilités XXXIII, volume 1709 of Lecture Notes in Math., pages 120–216. Springer, 1999.
77. M. Ledoux. The geometry of Markov diffusion generators. Ann. Fac. Sci. Toulouse Math. (6), 9:305–366, 2000.
78. M. Leitz-Martini. A discrete Clark-Ocone formula. Maphysto Research Report No 29, 2000.
79. J. León, J.L. Solé, and J. Vives. The chaos decomposition of functionals of the jump times for the Poisson process over a compact time interval. In Stochastic models (Guanajuato, 1998), pages 269–282. Soc. Mat. Mexicana, México, 1998. (Preprint 19/1998, september 1998, Universitat Autònoma de Barcelona).
80. J. León and C. Tudor. The chaos decomposition of the jump times for the Poisson process over a compact time interval. In L.G. Gorostiza, J.A. León, and J.A. López-Mimbela, editors, IV Simposio de Probabilidad y Procesos Estocásticos, volume 12 of Aportaciones Matemáticas, pages 137–146, Guanajuato, 1996. So-ciedad Matemática Mexicana.
81. J. Ma, Ph. Protter, and J. San Martin. Anticipating integrals for a class of martingales. Bernoulli, 4:81–114, 1998.
82. P. Major. Multiple Wiener-Itô integrals, volume 849 of Lecture Notes in Mathematics �Springer, Berlin, 1981.
83. P. Malliavin. Stochastic analysis, volume 313 of Grundlehren der Mathematis-chen Wissenschaften. Springer-Verlag, Berlin, 1997.
84. P. Malliavin and A. Thalmaier. Stochastic calculus of variations in mathematical finance. Springer Finance. Springer-Verlag, Berlin, 2006.
85. H.P. McKean. Geometry of differential space. Ann. Probability, 1:197–206, 1973.
86. J. Mecke. Stationäre zufällige Masse auf lokalkompakten Abelschen Gruppen. Z. Wahrscheinlichkeitstheorie Verw. Geb., 9:36–58, 1967.
87. M. Mensi and N. Privault. Conditional calculus on Poisson space and enlargement of filtration. Stochastic Anal. Appl., 21(1):183–204, 2003.
88. P.-A. Meyer and J. A. Yan. À propos des distributions sur l’espace de Wiener. In Séminaire de Probabilités XXI, volume 1247 of Lecture Notes in Mathematics, pages 8–26. Springer Verlag, 1987.
89. P.A. Meyer. Quantum Probability for Probabilists, volume 1538 of Lecture Notes in Mathematics. Springer-Verlag, 1993.
90. J. Neveu. Processus ponctuels. In Ecole d’été de Probabilités de Saint-Flour VI, volume 598 of Lecture Notes in Mathematics, pages 249–445. Springer-Verlag, 1977.
91. D. Nualart. Markov fields and transformations of the Wiener measure. In T. Lindstrøm, B. Øksendal, and A. S. Üstünel, editors, Proceedings of the Fourth Oslo-Silivri Workshop on Stochastic Analysis, volume 8 of Stochastics Monographs, Oslo, 1993. Gordon and Breach.
92. D. Nualart. The Malliavin Calculus and Related Topics. Probability and its Applications. Springer-Verlag, 1995.
93. D. Nualart and E. Pardoux. Stochastic calculus with anticipative integrands. Probab. Theory Related Fields, 78:535–582, 1988.
94. D. Nualart and J. Vives. Anticipative calculus for the Poisson process based on the Fock space. In Séminaire de Probabilités XXIV, volume 1426 of Lecture Notes in Math., pages 154–165. Springer, Berlin, 1990.
95. D. Nualart and J. Vives. A duality formula on the Poisson space and some applications. In R. Dalang, M. Dozzi, and F. Russo, editors, Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1993), volume 36 of Progress in Probability, pages 205–213. Birkhäuser, Basel, 1995.
96. D. Ocone. A guide to the stochastic calculus of variations. In H. Körezlioǧlu and A.S. Üstünel, editors, Stochastic Analysis and Related Topics, volume 1316 of Lecture Notes in Mathematics, pages 1–79, Silivri, 1988. Springer-Verlag.
97. B. Øksendal. An introduction to Malliavin calculus with applications to economics. Working paper no. 3, Institute of Finance and Management Science, Norwegian School of Economics and Business Administration, 1996.
98. B. Øksendal and F. Proske. White noise of Poisson random measures. Potential Anal., 21(4):375–403, 2004.
99. G. Peccati and C.A. Tudor. Anticipating integrals and martingales on the Poisson space. Random Oper. Stoch. Equ., 15(4):327–352, 2007.
100. J. Picard. Formules de dualité sur l’espace de Poisson. Ann. Inst. H. Poincaré Probab. Statist., 32(4):509–548, 1996.
101. G. Pisier. Probabilistic methods in the geometry of Banach spaces. In Probability and analysis (Varenna, 1985), pages 167–241. Springer, Berlin, 1986.
102. N. Privault. Chaotic and variational calculus in discrete and continuous time for the Poisson process. Stochastics and Stochastics Reports, 51:83–109, 1994.
103. N. Privault. Inégalités de Meyer sur l’espace de Poisson. C. R. Acad. Sci. Paris Sér. I Math., 318:559–562, 1994.
104. N. Privault. Calcul des variations stochastique pour les martingales. C. R. Acad. Sci. Paris Sér. I Math., 321:923–928, 1995.
105. N. Privault. Stochastic calculus of variations for martingales. In I. M. Davis, A. Truman, and K. D. Elworthy, editors, Proceedings of the Fifth Gregynog Symposium, Gregynog, 1995, pages 385–400. World Scientific, 1995.
106. N. Privault. Girsanov theorem for anticipative shifts on Poisson space. Probab. Theory Related Fields, 104:61–76, 1996.
107. N. Privault. On the independence of multiple stochastic integrals with respect to a class of martingales. C. R. Acad. Sci. Paris Sér. I Math., 323:515–520, 1996.
108. N. Privault. An extension of stochastic calculus to certain non-Markovian processes. Prépublication 49, Université d’Evry, 1997.
109. N. Privault. Independence of a class of multiple stochastic integrals. In R. Dalang, M. Dozzi, and F. Russo, editors, Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1996), volume 45 of Progress in Probability, pages 249–259. Birkhäuser, Basel, 1999.
110. N. Privault. Multiple stochastic integral expansions of arbitrary Poisson jump times functionals. Statistics & Probability Letters, 43:179–188, 1999.
111. N. Privault. On logarithmic Sobolev inequalities for normal martingales. Ann. Fac. Sci. Toulouse Math. (6), 9(3), 2000.
112. N. Privault. Distribution-valued gradient and chaotic decompositions of Poisson jump times functionals. Publicacions Matemàtiques, 46:27–48, 2002.
113. N. Privault. Stochastic analysis of Bernoulli processes. Probab. Surv., 5:435–483 (electronic), 2008.
114. N. Privault. Invariance of Poisson measures under random transformations. Preprint, 2009.
115. N. Privault and W. Schoutens. Discrete chaotic calculus and covariance identities. Stochastics and Stochastics Reports, 72:289–315, 2002. Eurandom Report 006, 2000.
116. N. Privault, J.L. Solé, and J. Vives. Chaotic Kabanov formula for the Azéma martingales. Bernoulli, 6(4):633–651, 2000.
117. N. Privault and X. Wei. A Malliavin calculus approach to sensitivity analysis in insurance. Insurance Math. Econom., 35(3):679–690, 2004.
118. N. Privault and X. Wei. Integration by parts for point processes and Monte Carlo estimation. J. Appl. Probab., 44:806–823, 2007.
119. Ph. Protter. Stochastic integration and differential equations. A new approach. Springer-Verlag, Berlin, 1990.
120. Ph. Protter. A partial introduction to financial asset pricing theory. Stochastic Process. Appl., 91(2):169–203, 2001.
121. Ph. Protter. Stochastic integration and differential equations, volume 21 of Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin, 2005.
122. D. Revuz and M. Yor. Continuous Martingales and Brownian Motion. Springer-Verlag, 1994.
123. Zd par le calcul des variations stochastiques. Ann. Inst. Henri Poincaré, Probab. Stat., 29(3):327–338, 1993.
124. J. Rosiński and G. Samorodnitsky. Product formula, tails and independence of multiple stable integrals. In Advances in stochastic inequalities (Atlanta, GA, 1997), volume 234 of Contemp. Math., pages 169–194. Amer. Math. Soc., Providence, RI, 1999.
125. J. Ruiz de Chávez. Predictable representation of the binomial process and application to options in finance. In XXXIII National Congress of the Mexican Mathematical Society (Spanish) (Saltillo, 2000), volume 29 of Aportaciones Mat. Comun., pages 223–230. Soc. Mat. Mexicana, México, 2001.
126. F. Russo and P. Vallois. Product of two multiple stochastic integrals with respect to a normal martingale. Stochastic Processes and their Applications, 73:47–68, 1998.
127. L. Saloff-Coste. Lectures on finite Markov chains. In Lectures on probability theory and statistics (Saint-Flour, 1996), volume 1665 of Lecture Notes in Math., pages 301–413. Springer, Berlin, 1997.
128. M. Sanz-Solé. Malliavin calculus with applications to stochastic partial differential equations. EPFL Press, Lausanne, 2005.
129. A.Ju. Ševljakov. Clark’s formula for discontinuous processes. In Behavior of systems in random media (Russian), pages 55–59. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1976.
130. A.Ju. Ševljakov. Integration of anticipating functionals. In Theory of random processes, No. 5 (Russian), pages 106–109, 115. Izdat. “Naukova Dumka”, Kiev, 1977.
131. A.Ju. Ševljakov. Stochastic differentiation and integration of functionals of a Wiener process. In Theory of random processes, No. 6 (Russian), pages 123–131, 136. “Naukova Dumka”, Kiev, 1978.
132. I. Shigekawa. Derivatives of Wiener functionals and absolute continuity of induced measures. J. Math. Kyoto Univ., 20(2):263–289, 1980.
133. I. Shigekawa. de Rham-Hodge-Kodaira’s decomposition on an abstract Wiener space. J. Math. Kyoto Univ., 26(2):191–202, 1986.
134. I. Shigekawa. Stochastic analysis, volume 224 of Translations of Mathematical Monographs. American Mathematical Society, Providence, RI, 2004.
135. A.N. Shiryaev. Essentials of stochastic finance. World Scientific Publishing Co. Inc., River Edge, NJ, 1999.
136. A.V. Skorokhod. On a generalization of a stochastic integral. Theor. Probab. Appl., XX:219–233, 1975.
137. J.L. Solé, F. Utzet, and J. Vives. Chaos expansions and Malliavin calculus for Lévy processes. In Stochastic analysis and applications, volume 2 of Abel Symp., pages 595–612. Springer, Berlin, 2007.
138. D. Stroock. Homogeneous chaos revisited. In Séminaire de Probabilités XXI, volume 1247 of Lecture Notes in Mathematics. Springer Verlag, 1987.
139. D. Stroock. Doing analysis by tossing a coin. Math. Intelligencer, 22(2):66–72, 2000.
140. D. Surgailis. On multiple Poisson stochastic integrals and associated Markov semi-groups. Probability and Mathematical Statistics, 3:217–239, 1984.
141. C. Tudor. A product formula for multiple Poisson-Itô integrals. Rev. Roumaine Math. Pures Appl., 42(3-4):339–345, 1997.
142. A.S. Üstünel. Representation of the distributions on Wiener space and stochastic calculus of variations. J. Funct. Anal., 70:126–139, 1987.
143. A.S. Üstünel. An introduction to analysis on Wiener space, volume 1610 of Lecture Notes in Mathematics. Springer Verlag, 1995.
144. A.S. Üstünel and M. Zakai. On the structure on independence on Wiener space. J. Funct. Anal., 90(1):113–137, 1990.
145. A.S. Üstünel and M. Zakai. Random rotations of the Wiener path. Probab. Theory Relat. Fields, 103(3):409–429, 1995.
146. A.S. Üstünel and M. Zakai. Transformation of measure on Wiener space. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2000.
147. S. Watanabe. Lectures on Stochastic Differential Equations and Malliavin Calculus. Tata Institute of Fundamental Research, 1984.
148. N. Wiener. The homogeneous chaos. Amer. Journ. Math., 55(4), 1938.
149. D. Williams. Probability with martingales. Cambridge Mathematical Textbooks. Cambridge University Press, Cambridge, 1991.
150. 1 and modified logarithmic Sobolev inequalities and deviation inequalities for Poisson point processes. Preprint, 1998.
151. L. Wu. A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probab. Theory Related Fields, 118(3):427–438, 2000.
152. M. Yor. Sur les intégrales stochastiques optionnelles et une suite remarquable de formules exponentielles. In Séminaire de Probabilités, X (Seconde par-tie: Théorie des intégrales stochastiques, Univ. Strasbourg, Strasbourg, année universitaire 1974/1975), pages 481–500. Lecture Notes in Math., Vol. 511. Springer, Berlin, 1976.
153. 1 et représentation des martingales. In Séminaire de Probabilités, XII, volume 649 of Lecture Notes in Math., pages 265–309. Springer, Berlin, 1978.