Laplace approximations for large deviations of diffusion processes on Euclidean spaces

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概要

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• Consider a class of uniformly elliptic diffusion processes { X_t }<SUB>t ≥ 0</SUB> on Euclidean spaces \bm{R}<SUP>d</SUP> . We give an estimate of E<SUP>P_x</SUP> \bigl[ exp (T ¶hi ({1}/{T} ∈t_0^T δ<SUB>X_t</SUB> dt)) \big| X_T =y \bigr] as T → ∞ up to the order 1 + o(1), where δ<SUB>•</SUB> means the delta measure, and ¶hi is a function on the set of measures on \bm{R}<SUP>d</SUP> . This is a generalization of the works by Bolthausen-Deuschel-Tamura \cite{B-D-T} and Kusuoka-Liang \cite{K-L_Torus}, which studied the same problems for processes on compact state spaces.

• 社団法人 日本数学会の論文
• 2005-04-01

著者

• Liang Song

  Graduate School Of Information Sciences Tohoku University

• Song Liang

  Graduate School Of Information Sciences Tohoku University

関連論文

• On an Ergodic Property of Diffusion Semigroups on Euclidean Space
• Laplace Approximations for Diffusion Processes on Torus: Nondegenerate Case
• On the Precise Laplace Approximation for Large Deviations of Markov Chain The Nondegenerate Case
• Large Deviation Principles for a Type of Diffusion Processes on Euclidean Space
• A mechanical model of Markov processes (Proceedings of RIMS Workshop on Stochastic Analysis and Applications)
• Laplace approximations for large deviations of diffusion processes on Euclidean spaces
• Laplace Approximations for Sums of Independent Random Vectors - The Degenerate Case -

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