学术报告通知

报告题目：On Small Noise Perturbations of Deterministic Dynamical Systems

报告人： 董昭 教授  （中国科学院数学与系统科学研究院）

报告时间：12月7日下午4点-5点

报告地点：数统院303

数学与统计学院

                                   2019.12.4

报告摘要：This talk presents a general framework to deal with the limit behavior of stationary measures for small noise perturbations of deterministic dynamical systems. Under the probability convergence assumption, we prove that any weak convergent limit of a sequence of stationary measures is an invariant measure of deterministic dynamical system, whose support is contained in the Birkhoff center of the deterministic dynamical system. This result can be applied to SODEs, SPDEs and SFDEs driven by either Brown motion or Levy process with small noise intensity as well as stochastic approximation with constant step. We also discuss stochastic stability and provide a criterion for a repeller to be a null set of limit measures for SODEs with small non-degenerate noise and prove that any limit cycle of a planar system with positive characteristic exponent is always a null set of limit measures. We show that there is a distinct difference on stochastic stability between noise perturbed systems of structurally stable and structurally unstable deterministic systems.

报告人简介： 董昭，中国科学院数学与系统科学研究院研究员，中国科学院大学岗位教授，北京航空航天大学数学科学院兼职教授。1990年北京师范大学数学系获硕士学位，1996年中国科学院应用数学研究所获博士学位。中国概率统计学会常务理事。 研究方向是：狄氏型与无穷维随机分析、 随机动力系统与随机偏微分方程、软件可靠性等。在国内、国外发表论文50 余篇,多篇论文发表在著名期刊J. Math. Pures Appl., J. Funct. Anal., J. Differential Equations, Probab. Theory Related Fields， Stochastic Process. Appl.等著名期刊上 。2006年以来主持5项国家自然基金项目，其中重点项目1项，并参与多项科研项目，如973项目、基金委的创新研究群体等。