報告題目：Weak Convergence Rates for an Explicit Full-Discretization of Stochastic Allen-Cahn Equation with Additive Noise
報 告 人：甘四清 教授 中南大學
報告時間：2023年12月5日 18:30-20:00
報告地點：騰訊會議 ID：672 708 241，密碼：544711
校内聯系人：鄒永魁 zouyk@jlu.edu.cn
報告摘要：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.
報告人簡介：甘四清，博士，中南大學二級教授，博士生導師。2001年畢業于中國科學院數學研究所，獲理學博士學位，2001-2003年在清華大學計算機科學與技術系高性能計算研究所從事博士後研究工作。主要研究方向為确定性微分方程和随機微分方程數值解法。主持國家自然科學基金面上項目5項，發表學術論文100餘篇。
