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Martingales, the Malliavin calculus and Hörmander's theorem

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Stochastic Integrals

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 851))

Abstract

The purpose of this paper is to give a new approach to the Malliavin calculus of variations using martingale techniques. The first part of the paper is devoted to the proof of an integration by parts formula, which is closely related to a martingale representation result of Haussmann. The second part of the paper is devoted to the proof of the existence of densities for the semi-group of a diffusion under slightly more general conditions than Malliavin, and the existence of densities for the resolvent operators under the general conditions of Hörmander.

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Authors and Affiliations

  1. Département de Mathématiques, Université Paris-Sud, 91405, Orsay

    Jean-Michel Bismut

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  1. Jean-Michel Bismut
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David Williams

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© 1981 Springer-Verlag

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Bismut, JM. (1981). Martingales, the Malliavin calculus and Hörmander's theorem. In: Williams, D. (eds) Stochastic Integrals. Lecture Notes in Mathematics, vol 851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088724

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  • DOI: https://doi.org/10.1007/BFb0088724

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10690-6

  • Online ISBN: 978-3-540-38613-1

  • eBook Packages: Springer Book Archive

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