题目：Fundamental Convergence Theorems of Numerical Methods for Stochastic Differential Equations

　　报告人：洪佳林 研究员 (中国科学院数学与系统科学研究院副院长，博士生导师)

　　时间：6月9日(星期一)下午4点

　　地点：数学楼一楼小报告厅

　　内容摘要：In this talk we review theoretical results on the mean-square convergence of numerical methods for stochastic ordinary differential equations, stochastic delay differential equations, neutral stochastic delay differential equations, jump-diffusion differential equations, neutral stochastic delay differential equations with jump-diffusion, stochastic partial differential equations. These results are called fundamental convergence theorems of numerical methods for stochastic differential equations. In this talk we propose a fundamental convergence theorem of semidiscretisation for stochastic Schroedinger equations in temporal direction. And based on Feynman-Kac type formula on backward stochastic differential equations, we present a fundamental convergence theorem of numerical methods for backward stochastic differential equations, and apply it to the mean-square convergence of numerical schemes for backward stochastic differential equations.