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题目:  Limiting Behavior of Stationary Measures for Stochastic Evolution Systems


报告人:  董昭 研究员 (中国科学院)


时间:  8月3日  上午 9:30-10:20


地点: 西大楼三楼报告厅


摘要: The limiting behavior of stochastic evolution processes with small noise intensity $\epsilon$ is investigated in distribution-based approach . Let $\mu^{\epsilon}$ be stationary measure for stochastic process $X^{\epsilon}$ with small $\epsilon$ and $X^{0}$ be a semiflow on a Polish space. Assume that $\{\mu^{\epsilon}:0<\epsilon<\epsilon_0\}$ is tight. Then all their weak$^*-$ limits are $X^0-$invariant and their supports are contained in Birkhoff center of $X^0$.  Applications are made to various stochastic evolution systems, including stochastic partial differential equations, stochastic functional differential equations, stochastic ordinary differential equations driven by Brownian motion or L$\acute{e}$vy process, as well as stochastic approximation with constant step.