From PDE Numerical Analysis to Robust Limit Theorems under Nonlinear Expectations

报告题目：From PDE Numerical Analysis to Robust Limit Theorems under Nonlinear Expectations

报告时间：2023年8月1日14:30-15:30

报告地点：红瓦楼723（暂定）

报告人：梁歌春 教授（University of Warwick）

报告摘要：The Feynman-Kac formula establishes the probabilistic representation of solutions to PDEs, linking the convergence of numerical schemes for PDEs to limit theorems in probability theory. In this talk, we extend this idea beyond linear settings to encompass nonlinear settings such as sublinear expectations (also known as Peng’s G-expectations) and convex expectations. We establish convergence rates for central limit theorems, laws of large numbers, and alpha-stable limit theorems under sublinear/convex expectations. Our approach employs the convergence analysis of viscosity solutions for corresponding fully nonlinear PDEs, focusing on the Barles-Souganidis monotone scheme analysis and the convergence rate analysis techniques developed by Krylov, Barles, and Jakobsen.

报告人简介：梁歌春博士是华威大学统计系的Reader。他过去的职位包括华威大学副教授、伦敦国王学院任终身教职，讲师和Oxford-Man量化金融研究所博士后研究员。2018-2019年荣获弗莱堡大学弗莱堡高等研究院（FRIAS）FRIAS高级研究员和玛利亚-居里研究员的称号。2011年获得牛津大学数学研究所数学博士学位。他的研究兴趣主要集中在金融数学和随机分析与控制，并在Annals of Probability、SIAM Journal on Control and Optimization、Finance and Stochastics、Mathematical Finance和SIAM Journal on Financial Mathematics等国际一流期刊发表了系列有影响的论文。

报告邀请人：徐承龙 教授