数学科学学院学术报告[2024] 082号

(高水平大学建设系列报告962号)

报告题目: Mean-field backward stochastic differential equations and nonlocal PDEs with quadratic growth

报告人：郝涛 副教授（山东财经大学）

报告时间：2024.08.16下午 16:00-17:00

讲座地点：科技楼 514

报告内容：In this talk, we study general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, the existence and uniqueness of local and global solutions are proved with some new ideas for a one-dimensional mean-field BSDE when the generator $g\big(t, Y, Z, \mathbb{P}_{Y}, \mathbb{P}_{Z}\big)$ has a quadratic growth in $Z$ and the terminal value is bounded. Second, a comparison theorem for the general mean-field BSDEs is obtained with the Girsanov transform. Third, we prove the convergence of the particle systems to the mean-field BSDEs with quadratic growth, and the convergence rate is also given. Finally, in this framework, we use the mean-field BSDE to provide a probabilistic representation for the viscosity solution of a nonlocal partial differential equation (PDE, for short) as an extended nonlinear Feynman-Kac formula, which yields the existence and uniqueness of the solution to the PDE.

报告人简历：郝涛，山东财经大学统计与数学学院副教授、硕士生导师。 2016 年在山东大学（威海）统计与数学学院获得博士学位。 多次到南方科技大学从事合作研究。主要研究领域为平均场正倒向随机微分方程、随机系统的最优控制和微分对策理论。 在国际重要学术期刊 ESAIM: COCV 、 Nonlinear Differential Equations and Applications 等发表多篇论文，并主持和参与多项国家级和省部级科研项目。

欢迎师生参加！

　　　　　　　　　　　　　　　　　　　　　　数学科学学院

　　　　　　　　　　　　　　　　　　　　 2024年08月14日