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