报告题目：Two-time-scale stochastic functional differential equations: Inclusion of infinite delay and coupled segment processes

报告人：吴付科 教授（华中科技大学）

邀请人：杨爽

报告时间：2025年12月24日15:00-16:00

报告地点：腾讯会议，会议号：265-133-932 会议密码：1037

参加人员：教师、研究生、本科生

报告摘要：This paper focuses on two-time-scale stochastic functional differential equations (SFDEs). It features in inclusion of infinite delay and coupling of slow and fast components. The coupling is through the segment processes of the slow and fast processes. The main difficulties include infinite delay and the coupling of segment processes involving fast and slow motions. Concentrating on weak convergence, the tightness of the segment process is established on a space of continuous functions. In addition, the Hölder continuity and boundedness for the segment process of the slow component, uniform boundedness for the segment process of a fixed-x SFDE, exponential ergodicity, and continuous dependence on parameters are obtained to carry out the desired asymptotic analysis, and also as byproducts, which are interesting in their own right. Then using the martingale problem formulation, an average principle is established by a direct averaging, which involves detailed computations and subtle estimates. Finally, two classes of special SFDEs, stochastic integro-differential equations and stochastic delay differential equations with two-time scales are investigated.

报告人简历：吴付科，教授、博士生导师，主要从事随机微分方程及其相关领域研究，2011年入选教育部新世纪优秀人才支持计划，2014年获得国家自然科学基金委员会优秀青年基金资助，2015年获得湖北省自然科学奖二等奖，2017年获得英国皇家学会牛顿高级学者基金，2025年主持国家自然科学基金重点项目。主要成果发表在主要成果发表在SIAM J. Appl. Math.、SIAM J. Numer. Anal.、SIAM J. Control Optim.、J. Differential Equations、Numer. Math.、Stoch. Proc. Appl.、Automatica和IEEE TAC等国际权威期刊。