报告人：吴付科 教授
报告题目：Weak Convergence for Two-Time-Scale McKean--Vlasov Systems
报告时间：2026年5月13日（周三）16:30-17:30
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
吴付科，华中科技大学数学与统计学院教授，博士生导师，国家优秀青年基金获得者，入选教育部新世纪优秀人才支持计划。主持国家自然科学基金委重点项目、面上项目、教育部新世纪优秀人才基金、英国皇家学会“高级牛顿学者”基金和美国数学学会（AMS）访问基金等。主要从事随机微分方程以及相关领域的研究。近年来，在SIAM系列杂志, JDE,SPA等期刊发表论文90余篇。
报告摘要：
This paper is concerned with the averaging principle for a class of two-time-scale McKean--Vlasov stochastic differential equations. Our analysis is concerned with weak solutions. The system under consideration consists of a slow component and a fast component. A salient feature here is that both the fast and slow dynamics depend on the distribution of the slow component. Using probabilistic methods, in particular, weak convergence methods, we aim to obtain averaging principles. The main difficulty lies in the low regularity of the coefficients together with the absence of dissipativity for the fast dynamics. To overcome these difficulties, we establish several tightness results and extend the occupation measure approach to the McKean--Vlasov setting. In addition, by virtue of the tightness arguments, we prove the continuity of the averaged coefficients, which is interesting in its own right. Combining the martingale problem formulation with a suitable frozen variable procedure, we then establish the desired averaging principle. Finally, we provide explicit conditions ensuring that the assumptions imposed on the system are satisfied. In particular, the classical dissipative condition and the partially dissipative condition both fall within our framework as special cases.