题目： Optimal feedback control problem for McKean-Vlasov SDEs

报告人：邵井海

讲座时间：2022年11月17日（星期四），14:30-15:30

地点：综合楼644会议室

交流平台：腾讯会议：730-849-918

报告人简介：

       邵井海，天津大学应用数学中心教授，博士生导师。2006年获得北京师范大学与法国第戎大学的理学博士学位。邵井海主要从事概率论遍历性理论、随机分析、随机微分方程方面的研究工作，在轨道空间和环空间上运输不等式、Monge-Kantorovich最优映射问题，以及带切换扩散过程长时间行为等问题的研究中取得了一些成果。

摘要：

This work concerns the optimal control problem for McKean-Vlasov SDEs.  Explicit sufficient conditions are given to ensure the existence of optimal feedback controls, and then the dynamic programming principle is established. In order to characterize the value function, as the state variable of the value function contains the probability measure, we use Mortensen's derivative to establish a Hamilton-Jacobi-Bellman equation on the Wasserstein space and show that the value function is a unique viscosity solution to this equation. In particular, a comparison principle is established for the associated viscosity sub- or super-viscosity solutions. Our approach is based on the heat kernel estimate of Gaussian type for the controlled diffusion processes.