Laplace's method for the laws of heat processes on loop spaces

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Abstract

In this paper, we will consider Laplace's method for a class of heat processes on loop spaces. We will obtain the first term of the asymptotics under assumptions that the function under consideration attains its minimum at a unique point and that the Hessian at the point is non-degenerate. This kind of process was first introduced by P. Malliavin in 1990 for the loop group case and then gradually generalized by various authors. Our tool is the rough path theory of T. Lyons. This technique was pioneered by S. Aida for finite-dimensional processes in his unpublished paper.

Original languageEnglish
Pages (from-to)148-194
Number of pages47
JournalJournal of Functional Analysis
Volume232
Issue number1
DOIs
Publication statusPublished - Mar 1 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis

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