An Averaging Principle for Two-Time-Scale Functional Diffusions

人工智能系列学术报告

报告题目：An Averaging Principle for Two-Time-Scale Functional Diffusions

报告人：吴付科 教授，博士生导师

报告时间：2020/10/20 10:00-11:00

报告形式：腾讯会议

会议ID：822 445 517

报告摘要：Dupire recently developed a functional It\^o formula, which has changed the landscape of the study of stochastic functional equations and encouraged a reconsideration of many problems and applications. Delays are ubiquitous, pervasive, and entrenched in everyday life. Based on the new development, this work examines functional diffusions with two-time scales in which the slow-varying process includes path-dependent functionals and the fast-varying process is a rapidly-changing diffusion. The gene expression of biochemical reactions occurring in living cells in the introduction of this paper is such a motivating example. This paper establishes mixed functional Ito formulas and the corresponding martingale representation. Then it develops averaging and weak convergence methods. By treating the fast-varying process as a random ``noise", under appropriate conditions, it is shown that the slow-varying process converges weakly to a stochastic functional differential equation whose coefficients are averages of that of the original slow-varying process with respect to the invariant measure of the fast-varying process.

报告人简介：

吴付科，华中科技大学教授，博士生导师。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”，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，期刊IET Control Theory & Applications编委，共主持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，出版一部专著和一部译著。