Laplace approximation for stochastic line integrals

Kazumasa Kuwada

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1-51
Number of pages51
JournalProbability Theory and Related Fields
Volume144
Issue number1-2
DOIs
Publication statusPublished - 2009 May

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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