Consider a class of uniformly elliptic diffusion processes $ \{ X_t \}_{t \ge 0} $ on Euclidean spaces $ \bm{R}^{d} $ . We give an estimate of $ E^{P_x} \left[ \exp (T \Phi ({1}/{T} \int_0^T \delta_{X_t} dt)) | X_T = y \right] $ as $ T \to \infty $ up to the order $ 1 + o(1) $ , where $ \delta_{\cdot} $ means the delta measure, and $ \Phi $ is a function on the set of measures on $\bm{R}^{d} $ . 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.
Publié le : 2005-04-14
Classification:
Laplace approximation,
large deviation,
diffusion process,
Euclidean space,
60F10,
60J60
@article{1158242071,
author = {LIANG, Song},
title = {Laplace approximations for large deviations of diffusion processes on Euclidean spaces},
journal = {J. Math. Soc. Japan},
volume = {57},
number = {4},
year = {2005},
pages = { 557-592},
language = {en},
url = {http://dml.mathdoc.fr/item/1158242071}
}
LIANG, Song. Laplace approximations for large deviations of diffusion processes on Euclidean spaces. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp. 557-592. http://gdmltest.u-ga.fr/item/1158242071/