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The probability functionals (Onsager-machlup functions) of diffusion processes

  • Y. Takahashi
  • S. Watanabe
Papers Based On Main Talks And Courses
Part of the Lecture Notes in Mathematics book series (LNM, volume 851)

Keywords

Stochastic Differential Equation Wiener Process Stochastic Integral Probability Functional Ideal Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    E. Cartan; Lecons sur la geometrie des espaces de Riemann, Gauthier-Villars, Paris, 1963MATHGoogle Scholar
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    D. Durr and A. Bach; The Onsager-Machlup function as Lagrangian for the most probable path of a diffusion process, Comm. Math. Phys. 60(1978) 153–170.MathSciNetCrossRefMATHGoogle Scholar
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    T.Fujita and S.Kotani; The Onsager-Machlup functions for diffusion processes, to appear.Google Scholar
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    R. Graham; Path integral formulation of general diffusion processes, Z. Physik B 26(1979), 281–290CrossRefGoogle Scholar
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    N. Ikeda and S. Manabe; Integral of differential forms along the path of diffusion processes, Publ. RIMS,Kyoto Univ. 15(1979), 827–852.MathSciNetCrossRefMATHGoogle Scholar
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    N.Ikeda and S.Watanabe; Stochastic differential equations and diffusion processes, Kodansha-John Wiley, 1980.Google Scholar
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    H. Ito; Probabilistic construction of Lagrangean of diffusion processes and its application, Prog.Theoretical Phys. 59(1978), 725–741.CrossRefMATHGoogle Scholar
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    H. Kunita and S. Watanabe; On square integrable martingales, Nagoya Math.J. 30 (1967), 209–245.MathSciNetCrossRefMATHGoogle Scholar
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    L. Onsager and S. Machlup; Fluctuations and irreversible processes, I, II, Phys. Rev. 91(1953), 1505–1512, 1512–1515.MathSciNetCrossRefMATHGoogle Scholar
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    R.L. Stratonovich; On the probability functional of diffusion processes, Select. Transl. in Math. Stat. Prob. 10(1971), 273–286.Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Y. Takahashi
    • 1
  • S. Watanabe
    • 2
  1. 1.University of TokyoJapan
  2. 2.Kyoto UniversityJapan

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