一、题目

An Averaging Principle for Two-Time-Scale Functional Diffusions

二、主讲人

吴付科

三、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.

四、主讲人简介

吴付科，华中科技大学数学与统计学院教授，博士生导师，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，SCI期刊《IET Control Theory & Applications》编委。

五、邀请人

陈章 数学学院教授

六、时间

12月4日（周五）10:00-11:00

七、地点

腾讯会议，会议ID：332594762

八、主办方

山东大学数学学院