報告時間：2025年10月13日（星期一）15:00
報告地點：翡翠湖校區科教樓B座1711室
報 告 人：吳付科 教授
工作單位：華中科技大學
舉辦單位：數學學院
報告簡介：
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 H?lder 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.
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。出版一部專著《隨機微分方程》和一部譯著《隨機微分方程：導論與應用》，當前為 IET Control Theory & Applications 編委。
