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Van Vleck-Pauli formula for Wiener integrals and Jacobi fields

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Itô’s Stochastic Calculus and Probability Theory

Abstract

In this paper, we are concerned with the explicit evaluation of Wiener integrals from the viewpoint of geometry of the space of paths. Our main purpose is to emphasize the close ties between explicit expressions of Wiener integrals associated with quadratic functionals and aspects of the theory of Jacobi fields.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Ritsumeikan University, Kusatsu, Shiga, 525-77, Japan

    Nobuyuki Ikeda

  2. Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan

    Shojiro Manabe

Authors
  1. Nobuyuki Ikeda
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  2. Shojiro Manabe
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Ritsumeikan University, 525-77, Kusatsu, Shiga, Japan

    Nobuyuki Ikeda (Professor) (Professor)

  2. Department of Mathematics, Graduate School of Science, Kyoto University, 606-01, Kyoto, Japan

    Shinzo Watanabe (Professor) (Professor)

  3. Department of Mathematics, Faculty of Fundamental Engineering, Osaka University, Toyonaka, Osaka, 560, Japan

    Masatoshi Fukushima (Professor) (Professor)

  4. Graduate School of Mathematics, Kyushu University, Fukuoka, 812, Japan

    Hiroshi Kunita (Professor) (Professor)

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© 1996 Springer-Verlag Tokyo

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Ikeda, N., Manabe, S. (1996). Van Vleck-Pauli formula for Wiener integrals and Jacobi fields. In: Ikeda, N., Watanabe, S., Fukushima, M., Kunita, H. (eds) Itô’s Stochastic Calculus and Probability Theory. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68532-6_9

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  • DOI: https://doi.org/10.1007/978-4-431-68532-6_9

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68534-0

  • Online ISBN: 978-4-431-68532-6

  • eBook Packages: Springer Book Archive

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