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The generalized Malliavin calculus based on Brownian sheet and Bismut's expansion for large deviation

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Stochastic Processes — Mathematics and Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1158))

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References

  1. Azencott, R., Grandes déviations et applications, Cours de Probabilité de Saint Flour, Lecture Notes in Math. vol. 774, Springer, Berlin, 1978.

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  2. Bismut, J.M., Large deviations and the Malliavin calculus, Progress in Math. vol. 45, Birkhäuser, Boston, Basel, Stuttgart, 1984.

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  3. Gaveau, B., Principe de moindre action, propagation de la chaleur, estimées sous-elliptiques sur certains groupes nilpotents, Acta Math. 139 (1977), 96–153.

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  4. Gross, L., Potential Theory on Hilbert Space, J. of Func. Analysis 1 (1967), 123–181.

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  5. Kusuoka, S., and Stroock, D., Applications of the Malliavin calculus, Part I, Stochastic Analysis, Proc. of the Taniguchi International Symp. Katata and Kyoto 1982, ed. K. Ito, Kinokuniya, Tokyo, 1984.

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  6. Malliavin, P. A., Calcul des variations stochastiques subordonné au processus de la chaleur, C. R. Acad. Sc. Paris Série I, t. 295 (1982), 167–172.

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  7. Molchanov, S. A., Diffusion processes and Riemanian geometry, Russian Math. Surveys 30 (1975), 1–53.

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Authors and Affiliations

  1. Department of Mathematics Faculty of Science, University of Tokyo, Japan

    Shigeo Kusuoka

Authors
  1. Shigeo Kusuoka
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Sergio A. Albeverio Philippe Blanchard Ludwig Streit

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© 1986 Springer-Verlag

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Kusuoka, S. (1986). The generalized Malliavin calculus based on Brownian sheet and Bismut's expansion for large deviation. In: Albeverio, S.A., Blanchard, P., Streit, L. (eds) Stochastic Processes — Mathematics and Physics. Lecture Notes in Mathematics, vol 1158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080214

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  • DOI: https://doi.org/10.1007/BFb0080214

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15998-8

  • Online ISBN: 978-3-540-39703-8

  • eBook Packages: Springer Book Archive

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