Southwest Jiaotong University School of Mathematics


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来源:   作者:方程与动力系统     日期:2020-11-20 20:08:26   点击数:  

题目: Strong Convergence of Euler-Maruyama Schemes for McKean-Vlasov Stochastic Differential Equations under Local Lipschitz Conditions of State Variables

报告人:吴付科 华中科技大学 教授 博士生导师

摘要: This paper develops the strong convergence for the Euler-Maruyama (EM) scheme to solve McKean-Vlasov stochastic differential equations (SDEs) by using interacting particle systems. In contrast to the existing work, a novel feature is that a much weaker condition, namely, local Lipschitzian in the state variable, is used. To obtain the desired result, one has to make sure the McKean-Vlasov SDE (the limit of the numerical approximation) has a unique solution. Thus, this paper first establishes the existence and uniqueness of solutions to the original McKean-Vlasov SDE under the one-sided local Lipschitz condition on the drift and the local Lipschitz condition on the diffusion coefficient of the state variable. The local Lipschitz constants of the drift and diffusion coefficients are of the orders $O(\log R)$ and $O(\sqrt{\log R})$, respectively, where $R$ is the radius of the neighborhood. To obtain the desired result, interpolated Euler-like sequence and partition of sample space are used to carry out the analysis. Then, the paper returns to the analysis of the EM scheme of system with empirical measures corresponding to the McKean-Vlasov SDE. A strong convergence theorem is established. This result much extends existing numerical results with the global conditions. Under additional conditions, the strong convergence rate can be obtained.

时间:  1123日(星期10:00-11: 00

地点:腾讯会议        会议 ID248 997 711

专家简介:吴付科,教授,博士生导师, 2003年博士毕业于华中科技大学数学与统计学院。主要从事随机微分方程以及相关领域的研究,2011年入选教育部新世纪优秀人才支持计划,2012年入选华中科技大学华中学者2014年获得基金委优秀青年基金资助,2015年获得湖北省自然科学二等奖,2017年获得英国皇家学会"牛顿高级学者"基金,《IET Control Theory & Applications》编委。近年来,发表论文80余篇,主持5项国家自然科学基金和一项教育部新世纪优秀人才基金,也主持过一项英国皇家学会高级牛顿学者基金和一项美国数学学会(AMS)基金。