TY - JOUR
T1 - Laplace's method for the laws of heat processes on loop spaces
AU - Inahama, Yuzuru
N1 - Funding Information:
This research was supported by JSPS Research Fellowships for Young Scientists. E-mail address: inahama@sigmath.es.osaka-u.ac.jp.
PY - 2006/3/1
Y1 - 2006/3/1
N2 - 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 This technique was pioneered by S. Aida for finite-dimensional processes in his unpublished paper.
AB - 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 This technique was pioneered by S. Aida for finite-dimensional processes in his unpublished paper.
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U2 - 10.1016/j.jfa.2005.06.006
DO - 10.1016/j.jfa.2005.06.006
M3 - Article
AN - SCOPUS:31044445671
SN - 0022-1236
VL - 232
SP - 148
EP - 194
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -