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：Mean-field backward stochastic differential equations and nonlocal PDEs with quadratic growth
报 告 人：胡瑛 教授 法国雷恩第一大学
报告时间：2025/7/2（周三） 16:30-17:30
报告地点：数学学院A321
报告摘要：In this talk, I will introduce general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, using some new ideas, we prove the existence and uniqueness of local and global solutions for a one-dimensional mean-field BSDE when the generator g(t,Y, Z, PY, PZ) has quadratic growth in Z and the terminal value is bounded. Second, we derive a comparison theorem for general mean-field BSDEs by applying the Girsanov transform. Third, within this framework, we use the mean-field BSDE to provide a probabilistic representation of the viscosity solution for 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. Finally, we prove the convergence of the particle systems to general mean-field BSDEs with quadratic growth and give the corresponding convergence rate.
报告人简介：胡瑛，法国雷恩一大特级教授，国际著名随机分析和随机控制专家，研究领域主要涉及随机过程、偏微分方程以及随机控制，特别是在倒向随机微分方程领域做出了卓越贡献。在PTRF、AAP、SICON、JFA、MF、FS、SPA等相关领域国际公认的顶尖权威杂志上发表高水平学术论文100余篇。