Laplace approximations for large deviations of diffusion processes on Euclidean spaces

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Abstract

Consider a class of uniformly elliptic diffusion processes (Xt)t ≥ 0 on Euclidean spaces Rd. We give an estimate of EPx[exp(TΦ(1/T ∫T0 δ Xt dt))||XT = y] as T → ∞ up to the order 1+o(1), where δ, means the delta measure, and Φ is a function on the set of measures on Rd. This is a generalization of the works by Bolthausen-Deuschel-Tamura [3] and Kusuoka-Liang [10], which studied the same problems for processes on compact state spaces.

Original languageEnglish
Pages (from-to)557-592
Number of pages36
JournalJournal of the Mathematical Society of Japan
Volume57
Issue number2
DOIs
Publication statusPublished - 2005
Externally publishedYes

Keywords

  • Diffusion process
  • Euclidean space
  • Laplace approximation
  • Large deviation

ASJC Scopus subject areas

  • Mathematics(all)

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