江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Fractional BSPDEs with Applications to Stochastic Optimal Control of Partially Observed Systems driven by Lévy Processes
报告人：李运章（复旦大学）
报告时间：2024年12月11日（周三）下午16:00-18:30
报告地点：腾讯会议ID：678-436-779
报告摘要：In this talk, we consider the Cauchy problem for backward stochastic partial differential equations (BSPDEs) involving fractional Laplacian operator. Firstly, by employing the martingale representation theorem and the fractional heat kernel, we construct an explicit form of the solution for fractional BSPDEs with space invariant coefficients, thereby demonstrating the existence and uniqueness of strong solution. Then utilizing the freezing coefficients method as well as the continuation method, we establish Hölder estimates and well-posedness for general fractional BSPDEs with coefficients dependent on space-time variables. As an application, we use the fractional adjoint BSPDEs to investigate stochastic optimal control of the partially observed systems driven by $\alpha$-stable Lévy processes. This is a joint work with Yuyang Ye and Shanjian Tang.
报告人简介：李运章，复旦大学智能复杂体系实验室青年副研究员。2020年博士毕业于复旦大学数学科学学院。2020年至2022年在复旦大学从事博士后研究工作，期间被聘为香港中文大学名誉博士后。主要研究领域为随机系统的最优控制问题的高阶精度数值算法，相关成果发表于SIAM J. Control. Optim., SIAM J. Sci. Comput., SIAM J. Financial Math., ESAIM: M2AN等知名学术期刊。入选上海市晨光计划，国家博士后创新人才支持计划，上海市“超级博士后”激励计划。主持国家自然科学基金委青年科学基金项目，上海市“科技创新行动计划”基础研究领域项目，中国博士后科学基金面上项目，获得复旦大学新工科人才基金资助。