Convergence and Dynamics of Random Differential Equations Driven by Stationary Process

主讲人：Kening Lu (吕克宁)  美国杨百翰大学，四川大学教授

时间：2019年5月15日10:00

地点：徐汇校区西部三号楼332

举办单位：数理学院

主讲人介绍：美国杨伯翰大学数学系教授、博导。1982年毕业于四川大学数学系，1988年毕业于美国密西根州立大学，获博士学位。2017年荣获首届“张芷芬数学成果奖”，2005年获中国国家杰出青年科学基金（B类）。研究方向为无穷维动力系统、非线性偏微分方程、随机偏微分方程。从1992年以来连续获得美国国家自然科学基金资助。多次应邀在重要的国际学术会议上作大会报告，美国《J.  Differential Equations》等国际著名学术期刊编委，已发表学术论文七十余篇，其中多篇刊发于世界数学一流杂志《Invent.  Math.》《Memoirs of AMS》《Communications on Pure and Applied  Mathematics》和《Transactions of AMS》等。

内容介绍：We study the convergence and pathwise dynamics of random differential equations  driven by a stationary process such as Euler approximation of Brownian motion  and colored noise. We first show that the solutions of these random differential  equations with a nonlinear diffusion term uniformly converge in mean square to  the solutions of the corresponding Stratonovich stochastic differential equation  as the correlation time of noise approaches zero. Then, we construct random  center manifolds for such random differential equations and prove that these  manifolds converge to the random center manifolds of the corresponding  Stratonovich equations. Finally, we consider the chaotic behavior of  differential equations with a homoclinic loop under an unbounded random forcing  driven by a Brownian motion and that for a set of full measure in the classical  Wiener space, the forced equation admits a topological horseshoe of infinitely  many branches.