报告时间：2025年10月13日（星期一）15:00-16:00

报告地点：翡翠科教楼B座1711室

报  告  人：吴付科 教授

工作单位：华中科技大学

举办单位：数学学院

报告简介：

This paper investigates near-optimal controls for a class of fully-coupled stochastic functional differential equations (SFDEs) with two-time scales, in which all coefficients depend on the segment processes of both the fast and slow components. The underlying problem is to minimize a cost functional subject to the SFDEs mentioned above. Our primary tools are probabilistic methods, in particular, weak convergence methods. The main challenge lies in the complete coupling of the fast and slow processes through their segment processes along with the resulting effects on the tightness of the segment process of the slow component. To address these challenges, the boundedness and Holder continuity for such segment process are established in a continuous function space. In addition, it is also shown that the segment process of a fixed-x SFDE is uniformly bounded, exponentially ergodic, and continuously dependent on the parameter x. By using the relaxed control representation and the martingale problem formulation, it is proved that the slow process and the corresponding value function in the original problem converge to that of a limit problem, where the coefficients of the limit problem are obtained by averaging coefficients of the original problem with respect to the invariant measure of the fixed-x equation. Finally, by solving the optimal control problem for the limit problem, a practically useful control for the original system is constructed. Such constructed controls are shown to be nearly optimal for the original problem.

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。出版一部专著《随机微分方程》和一部译著《随机微分方程：导论与应用》，当前为《IET Control Theory & Applications》编委。