報告人：吳付科 教授
報告題目：Weak Convergence for Two-Time-Scale McKean--Vlasov Systems
報告時間：2026年5月13日（周三）16:30-17:30
報告地點：云龍校區6號樓304報告廳
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
吳付科，華中科技大學數學與統計學院教授，博士生導師，國家優秀青年基金獲得者，入選教育部新世紀優秀人才支持計劃。主持國家自然科學基金委重點項目、面上項目、教育部新世紀優秀人才基金、英國皇家學會“高級牛頓學者”基金和美國數學學會（AMS）訪問基金等。主要從事隨機微分方程以及相關領域的研究。近年來，在SIAM系列雜志, JDE,SPA等期刊發表論文90余篇。
報告摘要：
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.