报告人：邵井海教授(天津大学，“全国百篇优秀博士学位论文奖”获得者)

报告题目：Invariant Measures for Path-Dependent Random Diffusions

报告摘要：In this talk, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment characterized by a continuous time Markov chain. Under certain ergodic conditions, we show that the path-dependent random diffusion enjoys a unique invariant probability measure and converges exponentially to its equilibrium under the Wasserstein distance. Also, we demonstrate that the time discretization of the path-dependent random diffusion involved admits a unique invariant probability measure and shares the corresponding ergodic property when the stepsize is sufficiently small. During this procedure, the difficulty arose from the time-discretization of continuous time Markov chain has to be deal with, for which an estimate on its exponential functional is presented.

报告人简介：邵井海教授于2006年获得北京师范大学与法国第戎大学的理学博士学位，同年在北京师范大学留校任教。2010年被聘为副教授。2007年，赴德国伯恩大学跟随K. Sturm教授做两年博士后研究。2017年被天津大学聘为教授。  主要从事概率论遍历性理论、随机分析、随机微分方程方面的研究工作。多篇论文发表在著名数学刊物，包括J. Functional Analysis, Probability Theory and Related Fields, SIAM J. Control Optim, SIAM J. Math. Anal., Stochastic Processes and their Applications。 2007年，邵井海教授获得中国数学学会“钟家庆数学奖”，2008年，获得“全国百篇优秀博士学位论文奖”

报告时间：2017年11月16日(星期四)下午：16:00-17:00

报告地点：科技楼(南楼)602