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

作　　者：Lifeng Chen Zhao Dong Jifa Jiang Jianliang Zhai 

机构地区：[1]Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]Wu Wen-Tsun Key Laboratory of Mathematics,University of Science and Technology of China,Hefei 230026,China

出　　处：《Science China Mathematics》2020年第8期1463-1504,共42页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11771295,11271356,11371041,11431014 and 11401557);Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,and the Fundamental Research Funds for the Central Universities(Grant No.WK0010000048)。

摘　　要：The limiting behavior of stochastic evolution processes with small noise intensityεis investigated in distribution-based approaches.Letμεbe a stationary measure for stochastic process Xεwith smallεand X0 be a semiflow on a Polish space.Assume that{με:0<ε≤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 Levy processes.

关 键 词：stationary measure Lyapunov function limit measure support Birkhoff center stochastic evolution system 

分 类 号：O211.63[理学—概率论与数理统计]