报告题目: Numerical approximation of random and stochastic (partial) differential equations
报告人: Prof. Peter Kloeden
Higher order numerical schemes for stochastic differential equations (SODEs) can be derived systematically using stochastic Taylor expansions based on iterated applications of the It\^o formula. For stochastic partial differential equations (SPDEs) there is no general It\^o formula that can be used in this way. Nevertheless higher order temporal expansions for mild solutions of SPDEs are possible using Taylor-like expansions with an idea that was first used for pathwise random ordinary differential equations (RODEs). This will be illustrated first for RODEs and then extended to SPDEs. The same relationship between RODEs and SODES as well as RPDEs and SPDEs will be indicated as well as other issues that arise in their discretization.
Prof. Dr. P.E. Kloeden是随机微分方程数值解和随机动力系统等研究方向的国际知名专家，其与人合著的著作《Numerical solution of stochastic differential equations》在Google学术中的引用超过6000次。Kloeden教授先后在澳大利亚 Deakin大学、德国Frankfurt大学任教授，现为华中科技大学数学与统计学院的“外专千人计划”特聘教授。曾担任SIAM J. Numerical Analysis、Foundation of Computational Mathematics、Nonlinear Analysis: Theory, Methods and Applications等国际著名期刊编委。现为杂志Discrete and Continuous Dynamical Systems-Series B的主编, 担任Journal of Difference Equations and Applications、Stochastics & Dynamics、Advanced Nonlinear Studies等十余种杂志的编委。