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Lagrangian for pinned diffusion process

In: Itô’s Stochastic Calculus and Probability Theory

Author

Listed:
  • Keisuke Hara

    (University of Tokyo, Graduate School of Mathematical Sciences)

  • Yoichiro Takahashi

    (Kyoto University, Research Institute for Mathematical Science)

Abstract

In the 1960s Professor K. Itô tried to understand the Feynman path integral probabilistically and constructed its integral representation over time dependent Hilbert spaces ([11], also [10]). Near the end of the 1970s D.Fujiwara succeeded in proving the existence of the limit of finite dimensional path integrals for Schrödinger equations in a very strong sense [3], and later in showing “Itô’s version” [4]. Inspired by their works and looking at the discussions on the effect of curvature among physicists, one of the authors started studying the problem of most probable path or the Lagrangian or the Onsager-Machlup function or the probability functional for diffusion process on manifolds (cf., e.g., [5],[16]), and which is completely determined by a collaboration with S. Watanabe [18] (see Theorem 1.2 below).

Suggested Citation

  • Keisuke Hara & Yoichiro Takahashi, 1996. "Lagrangian for pinned diffusion process," Springer Books, in: Nobuyuki Ikeda & Shinzo Watanabe & Masatoshi Fukushima & Hiroshi Kunita (ed.), Itô’s Stochastic Calculus and Probability Theory, pages 117-128, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-68532-6_7
    DOI: 10.1007/978-4-431-68532-6_7
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