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Onsager-Machlup functionals for solutions of stochastic boundary value problems

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Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1613)

Abstract

The purpose of this paper is to compute the asymptotic probability that the solution of a stochastic differential equation with boundary conditions belongs to a small tube of radius ≠>0 centered around the solution of the deterministic equation without drift.

Keywords

  • Brownian Motion
  • Stochastic Differential Equation
  • Exit Time
  • Deterministic Equation
  • Wiener Space

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.

The work of D. Nualart was done during his staying at the Laboratoire de Probabilités, Univ. Paris VI.

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References

  1. M. Chaleyat-Maurel and D. Nualart: The Onsager-Machlup functional for a class of anticipating processes. Probab. Theory Rel. Fields 94, 247–270 (1992).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. I. Chavel: Eigenvalues in Riemannian Geometry. Academic Press, 1984.

    Google Scholar 

  3. N. Ikeda and S. Watanabe: Stochastic differential equations and Diffusion processes, Amsterdam, Oxford, New York: North-Holland, 1981.

    MATH  Google Scholar 

  4. S. Kusuoka: The non linear transformation of Gaussian measure on Banach space and its absolute continuity. (I). J. Fac. Sci. Tokyo Univ. 32 Sec. IA, 567–597 (1985)

    MATH  Google Scholar 

  5. Wenbo Li: Private communication.

    Google Scholar 

  6. D. Nualart and E. Pardoux: Stochastic calculus with anticipating integrands. Probab. Theory Rel. Fields 78, 535–581 (1988).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. D. Nualart and E. Pardoux: Boundary value problems for stochastic differential equations. Annals of Probability 19, 1118–1144 (1991).

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. D. Nualart and E. Pardoux: Second order stochastic differential equations with Dirichlet boundary conditions. Stochastic Processes and Their Applications, 39, 1–24 (1991).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. D. Nualart and E. Pardoux: Stochastic differential equations with boundary conditions. In: Stochastic Analysis and Appl. ed. A.B. Cruzeiro and J.C. Zambrini. Birkhauser 1991, 155–175.

    Google Scholar 

  10. L.A. Shepp and O. Zeitouni: A note on conditional exponential moments and Onsager Machlup functionals. Annals of Probability 20, 652–654 (1992).

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1995 Springer-Verlag

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Chaleyat-Maurel, M., Nualart, D. (1995). Onsager-Machlup functionals for solutions of stochastic boundary value problems. In: Azéma, J., Emery, M., Meyer, P.A., Yor, M. (eds) Séminaire de Probabilités XXIX. Lecture Notes in Mathematics, vol 1613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094199

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  • DOI: https://doi.org/10.1007/BFb0094199

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60219-4

  • Online ISBN: 978-3-540-44744-3

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