Random perturbations of nonlinear oscillators
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; Technische Universitat Dresden
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1998
页码：
925-967
关键词：
摘要：
Degenerate white noise perturbations of Hamiltonian systems in R-2 are studied. In particular perturbations of a nonlinear oscillator with 1 degree of freedom are considered. If the oscillator has more than one stable equilibrium, the long time behavior of the system is defined by a diffusion process on a graph. Inside the edges the process is defined by a standard averaging procedure, but to define the process for all t > 0, one should add gluing conditions at the vertices. Calculation of the gluing conditions is based on delicate Hormander-type estimates.