报告题目：Weak Convergence Rates for an Explicit Full-Discretization of Stochastic Allen-Cahn Equation with Additive Noise
报 告 人：甘四清 教授 中南大学
报告时间：2023年12月5日 18:30-20:00
报告地点：腾讯会议 ID：672 708 241，密码：544711
校内联系人：邹永魁 zouyk@jlu.edu.cn
报告摘要：We discretize the stochastic Allen-Cahn equation with additive noise by means of a spectral Galerkin method in space and a tamed version of the exponential Euler method in time. The resulting error bounds are analyzed for the spatio-temporal full discretization in both strong and weak senses. Different from existing works, we develop a new and direct approach for the weak error analysis, which does not rely on the use of the associated Kolmogorov equation or Itô’s formula and is therefore non-Markovian in nature. Such an approach thus has a potential to be applied to non-Markovian equations such as stochastic Volterra equations or other types of fractional SPDEs, which suffer from the lack of Kolmogorov equations. It turns out that the obtained weak convergence rates are, in both spatial and temporal direction, essentially twice as high as the strong convergence rates. Also, it is revealed how the weak convergence rates depend on the regularity of the noise. Numerical experiments are finally reported to confirm the theoretical conclusion.
报告人简介：甘四清，博士，中南大学二级教授，博士生导师。2001年毕业于中国科学院数学研究所，获理学博士学位，2001-2003年在清华大学计算机科学与技术系高性能计算研究所从事博士后研究工作。主要研究方向为确定性微分方程和随机微分方程数值解法。主持国家自然科学基金面上项目5项，发表学术论文100余篇。
