On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity

• 作者: Jianliang Zhai Jifa Jiang Lifeng Chen Zhao Dong
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（8）
• 所属期刊栏目: Progress of Projects Supported by NSFC
• 页码范围: 1463-1504
• 页数: 42页
• 语种: 英文

摘要

The limiting behavior of stochastic evolution processes with small noise intensity ε is investigated in distribution-based approaches.Let με be a stationary measure for stochastic process Xε with small ε and X0 be a semiflow on a Polish space.Assume that {με : 0 ＜ e ≤ ε0} is tight.Then all their limits in the weak sense are X0-invariant and their supports are contained in the Birkhoff center of X0.Applications are made to various stochastic evolution systems,including stochastic ordinary differential equations,stochastic partial differential equations,and stochastic functional differential equations driven by Brownian motion or Lévy processes.