Random perturbations of dynamical systems and diffusion processes with conservation laws
成果类型：
Article
署名作者：
Freidlin, M; Weber, M
署名单位：
University System of Maryland; University of Maryland College Park
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-003-0312-0
发表日期：
2004
页码：
441-466
关键词：
摘要：
In this paper we consider random perturbations of dynamical systems and diffusion processes with a first integral. We calculate, under some assumptions, the limiting behavior of the slow component of the perturbed system in an appropriate time scale for a general class of perturbations. The phase space of the slow motion is a graph defined by the first integral. This is a natural generalization of the results concerning random perturbations of Hamiltonian systems. Considering diffusion processes as the unperturbed system allows to study the multidimensional case and leads to a new effect: the limiting slow motion can spend non-zero time at some points of the graph. In particular, such delay at the vertices leads to more general gluing conditions. Our approach allows one to obtain new results on singular perturbations of PDE's.