一、报告题目

Empirical Approximation to Invariant Measures for McKean-Vlasov Processes

二、主讲人

杜 恺

三、报告时间

2022年10月25日 18:00-19:00

四、报告地点

ZOOM ID

五、摘要

This work obtains that, under a monotonicity condition, the invariant probability measure of a McKean-Vlasov process can be approximated by weighted empirical measures of some processes including itself. These processes are described by distribution dependent or empirical measure dependent stochastic differential equations constructed from the equation for the McKean-Vlasov process. Convergence of empirical measures is characterized by upper bound estimates for their Wasserstein distance to the invariant measure. The theoretical results are demonstrated via a mean-field Ornstein-Uhlenbeck process.

六、主讲人简介

杜恺，复旦大学上海数学中心青年研究员、博士生导师，国家优秀青年基金获得者，上海市东方学者特聘教授；2011年获复旦大学博士学位，曾任职于苏黎世联邦理工学院(ETH)、澳大利亚Wollongong大学；长期从事概率论、偏微分方程、最优控制、强化学习等理论与应用的研究，成果发表于PTRF、TAMS、SICON、JDE等国际主流期刊；主持和参与多项国家级、省部级科研项目。

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心