On Stochastic Stability of Ordinary Differential Equations

讲座时间 Datetime: 2022年11月14日，星期一，15:00-16:30

地点 Venue: 腾讯线上会议：301-604-467

主持人 Host：赵育林 教授

报告人 Speaker: 蒋继发 教授

单位 Affiliation: 上海师范大学

报告摘要 Abstract:

We exploit limiting measures of stationary measures of stochastic ordinary differential equations. 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. This implies that any limiting measure will concentrated on Liapunov stable compact invariant sets if unperturbed ordinary differential equations are dissipative. Applications are made to the

Morse-Smale systems, the Axiom A systems including structural stability systems and separated start systems, the gradient or gradient-like systems, those systems possessing the Poincaré-Bendixson property with a finite number of limit sets to obtain that limiting measures live on Liapunov stable critical elements, Liapunov stable basic sets, Liapunov stable equilibria, Liapunov stable limit sets including saddle or trap cycles, respectively. Together these results with the Laplace method, we give the exact concentration of limiting measure of quasipotential systems, which is the support of stochastically stable invariant measure. This is a joint work with Chen Lifeng and Xu Tianyuan.

报告人简介：上海师范大学教授，1989年7月于中国科学院数学研究所获博士学位, 获首届中国科学院院长奖学金特别奖. 1992年被国家人事部评为有突出贡献的中青年专家, 并获(国务院)政府特殊津贴; 1993年分获安徽省科技进步奖二等奖(独人承担)和曾宪梓教育基金奖; 1994年获中国科学技术大学首届《跨世纪优秀人才奖》; 2004-2006连续三年被中国科学院评为“优秀研究生指导导师”；培养了两名博士生分获2004、2006年教育部全国百篇优秀论文(两人随后入选教育部新世纪优秀人才计划, 其中一位于2012年入选首届中共中央组织部青年拔尖人才计划). 曾为安徽省政协第七, 第八和第九届委员会委员.自从1993年以来持续主持国家自然科学基金委面上项目、参加两项国家自然科学基金委重点项目；主持多项国家教委（教育部）、科学院、上海市科委和教委项目。