Self-interacting diffusions. III. Symmetric interactions
成果类型：
Article
署名作者：
Benaïm, M; Raimond, O
署名单位：
University of Neuchatel; Universite Paris Saclay
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117905000000251
发表日期：
2005
页码：
1716-1759
关键词：
摘要：
Let M be a compact Riemannian manifold. A self-interacting diffusion on M is a stochastic process solution to where {W-t} is a Brownian vector field on M and V-x(y) = V(x, y) a smooth function. Let mu(t) = 1/t integral(t)(0) delta X-s ds denote the normalized occupation measure of X-t. We prove that, when V is symmetric, mu(t) converges almost surely to the critical set of a certain nonlinear free energy functional J. Furthermore, J has generically finitely many critical points and mu(t) converges almost surely toward a local minimum of J. Each local minimum has a positive probability to be selected.