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Laplace approximation for stochastic line integrals
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  • Published: 19 February 2008

Laplace approximation for stochastic line integrals

  • Kazumasa Kuwada1 

Probability Theory and Related Fields volume 144, pages 1–51 (2009)Cite this article

Abstract

We prove a precision of large deviation principle for current-valued processes such as shown in Bolthausen et al. (Ann Probab 23(1):236–267, 1995) for mean empirical measures. The class of processes we consider is determined by the martingale part of stochastic line integrals of 1-forms on a compact Riemannian manifold. For the pair of the current-valued process and mean empirical measures, we give an asymptotic evaluation of a nonlinear Laplace transform under a nondegeneracy assumption on the Hessian of the exponent at equilibrium states. As a direct consequence, our result implies the Laplace approximation for stochastic line integrals or periodic diffusions. In particular, we recover a result in Bolthausen et al. (Ann Probab 23(1):236–267, 1995) in our framework.

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Authors and Affiliations

  1. Graduate School of Humanities and Sciences, Ochanomizu University, Tokyo, 112-8610, Japan

    Kazumasa Kuwada

Authors
  1. Kazumasa Kuwada
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Correspondence to Kazumasa Kuwada.

Additional information

Partially supported by JSPS Fellowship for young scientists.

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Cite this article

Kuwada, K. Laplace approximation for stochastic line integrals. Probab. Theory Relat. Fields 144, 1–51 (2009). https://doi.org/10.1007/s00440-008-0140-3

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  • Received: 01 June 2005

  • Revised: 11 January 2008

  • Published: 19 February 2008

  • Issue Date: May 2009

  • DOI: https://doi.org/10.1007/s00440-008-0140-3

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Keywords

  • Laplace approximation
  • Large deviation
  • Stochastic line integral
  • Empirical measure

Mathematics Subject Classification (2000)

  • 60F10
  • 60B10
  • 60B12
  • 58J65
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