报告题目：Stochastic methods for semi-linear PDEs driven by α-stable Lévy process

报告人：盛长滔博士 (上海财经大学)

报告时间：2024年06月29日上午10:00-11:00

报告地点：数学楼2-3会议室

报告摘要：In this talk, we introduce the Monte Carlo methods for solving high dimensional PDEs driven by α-stable Lévy process. The main idea behind our approach is to divide the time interval into N sub-intervals and derive the Feynman-Kac formula within each time sub-interval. Then, we develop a fully discretized parallel scheme using the implicit-explicit technique for temporal discretization, followed by applying a novel walk-on-sphere method to obtain the numerical solution. Notably, the proposed method takes advantage of the Poisson kernel associated with the stochastic processes to accommodate the full discretization of the classical and fractional semi-linear PDEs in a single framework. Moreover, we rigorously analyze the error bound for the proposed scheme that is explicit with respect to the number of simulation paths and the time step size. Ample numerical results are presented to demonstrate the robustness and effectiveness of the proposed method.

报告人简介：盛长滔，上海财经大学，2018年于厦门大学获得理学博士学位，之后在新加坡南洋理工大学从事博士后研究。主要研究方向为谱方法和谱元法以其应用、高维偏微分方程的随机算法等。主持国家自然科学青年基金和上海市浦江人才计划等项目。目前为止，在SIAM J. Numer. Anal., Math. Comp., ESAIM M2AN.等知名国内外期刊上发表多篇论文。