数学科学学院学术报告[2024] 066号

(高水平大学建设系列报告946号)

报告题目: Stochastic Differential Games with Random Coefficients and Stochastic Hamilton-Jacobi-Bellman-Isaacs Equations

报告人：张静，副教授，复旦大学

报告时间：2024.07.17下午15:30-16:30

讲座地点：汇星楼（科技楼）514

报告内容：We study a class of zero-sum two-player stochastic differential games with the controlled stochastic differential equations and the payoff/cost functionals of recursive type. As opposed to the pioneering work by Fleming and Souganidis [Indiana Univ. Math. J., 1989] and the seminal work by Buckdahn and Li [SIAM J. Control Optim., 2008], the involved coefficients may be random, going beyond the Markovian framework and leading to the random upper and lower value functions. We first prove the dynamic programming principle for the game, and then under the standard Lipschitz continuity assumptions on the coefficients, the upper and lower value functions are shown to be the viscosity solutions of the upper and the lower fully nonlinear stochastic Hamilton-Jacobi-Bellman-Isaacs equations, respectively.  A stability property of viscosity solutions is also proved. Under certain additional regularity assumptions on the diffusion coefficient, the uniqueness of the viscosity solution is addressed as well.

报告人简历： 张静，复旦大学数学科学学院副教授，2012年法国埃夫里大学应用数学博士学位，2013年进入复旦大学至今。主要研究领域随机偏微分方程、倒向随机微分方程、随机控制等，在AOP，AAP，SPA，JDE等杂志发表论文十余篇。

邀请人：王寒霄

欢迎师生参加！

                                         数学科学学院

                                         2024年07月15日