报告题目： On the Stochastic Stability of Limiting Measures in SODEs 

报告人： 蒋继发教授， 上海师范大学

腾讯会议：261-191-026

报告时间： 2021年12月3日下午： 2：00 - -3：00

报告摘要： We exploit limiting measures of stationary measures of stochastic ordinary differential equations (SODEs). Such measures are more stable than other invariant measures of unperturbed systems or the most stable if they uniquely exist to stochastic perturbations. Using the Freidlin-Wentzell large deviations principle, we prove that limiting measures are concentrated away from repellers which are topologically transitive, or equivalent classes, or admit Lebesgue measure zero. We also preclude concentrations of limiting measures on acyclic saddle or trap chains. Applications are made to the Morse-Smale systems, the Axiom A systems, the gradient or gradient-like systems, those systems possessing a finite number of limit sets to obtain that limiting measures live on Liapunov stable critical elements, Liapunov stable basic sets or cycles of basic sets, Liapunov stable equilibria, Liapunov stable limit sets including saddle or trap cycles, respectively. A number of nontrivial examples admitting a unique limiting measure are provided. This illustrates that Liapunov unstable invariant sets cannot stand the disturbance of arbitrary nondegenerate noise, while some of Liapunov stable invariant sets indeed can! This is a joint work with Xu Tianyuan and Chen Lifeng.

腾讯会议：261-191-026

邀请人：廖刚