Summary
In this paper we study the conditional independence of sigma-fields on the Wiener space using the tools of the Stochastic Calculus of Variations. Particular emphasis is given to the relation between the splitting of the (random) tangent spaces associated to the sigma-fields and the conditional independence.
References
Ikeda, N., Watanabe, S.: An introduction to Malliavin's Calculus. Proceedings of Taniguchi Inter. Symposium on Stochastic Analysis, Kataka-Kyoto, 1982, pp. 1–52. Tokyo, Amsterdam: Kinokuniya North-Holland 1984
Nualart, D., Ustunel, A.S., Zakai, M.: Some relations among classes of σ-fields on Wiener space. Probab. Th. Rel. Fields85, 119–129 (1990)
Nualart, D., Zakai, M.: Generalized stochastic integrals and the Malliavin Calculus. Probab. Th. Rel. Fields73, 255–280 (1986)
Nualart, D., Zakai, M.: The partial Malliavin calculus. Séminaire de Probabilités XXIII (Lect. Notes Math., vol. 1372, pp. 362–381) Berlin Heidelberg New York: Springer 1989
Ustunel, A.S., Zakai, M.: On independence and conditioning on Wiener space. Ann. Probab.17, 1441–1453 (1989)
Ustunel, A.S., Zakai, M.: On the structure of independence on Wiener space. J. Funct. Anal.90, 113–137 (1990)
Ustunel, A.S.: Construction du calcul d'Itô sur l'espace de Wiener abstrait. C.R. Acad. Sci., Paris, Sér. I305, 279–282 (1987)
Watanabe, S.: Lectures on stochastic differential equations and Malliavin Calculus (Tata Institute Lectures on Mathematics). Berlin Heidelberg New York: Springer 1984
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Partially supported by the CICYT grant no PB86-0238
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Nualart, D., Ustunel, A.S. Geometric analysis of conditional independence on Wiener space. Probab. Th. Rel. Fields 89, 407–422 (1991). https://doi.org/10.1007/BF01199786
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DOI: https://doi.org/10.1007/BF01199786
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Tangent Space
- Conditional Independence