Speaker: Jialin Hong, Chinese Academy of Sciences

Time: July 20, 11:00-11:40

Address: Room 327, 3rd floor, New Activity Center, HIT

Title: Fundamental Convergence of Numerical Methods for Stochastic Differential Equations

Abstract: 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.