江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：Mean-field backward stochastic differential equations and nonlocal PDEs with quadratic growth
報 告 人：胡瑛 教授 法國雷恩第一大學
報告時間：2025/7/2（周三） 16:30-17:30
報告地點：伟德bvA321
報告摘要：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.
報告人簡介：胡瑛，法國雷恩一大特級教授，國際著名随機分析和随機控制專家，研究領域主要涉及随機過程、偏微分方程以及随機控制，特别是在倒向随機微分方程領域做出了卓越貢獻。在PTRF、AAP、SICON、JFA、MF、FS、SPA等相關領域國際公認的頂尖權威雜志上發表高水平學術論文100餘篇。