[Lecture] CAM Seminar— Fundamental convergence theorem of numerical methods for stochastic systems
Title: CAM Seminar— Fundamental convergence theorem of numerical methods for stochastic systems
Time: 15:30-16:30, Nov. 13, 2018, Tuesday
Venue: Room 1303, Sciences Building No. 1
Speaker: Prof. Chuchu Chen (LSEC, AMSS)
Abstract: In the numerical analysis of stochastic ordinary differential equations (SODEs), G. N. Milstein proposed an important convergence criterion to evaluate the mean-square convergence order for numerical approximations of SODEs, which is called fundamental convergence theorem. Motivated by Milstein’s work, we proposed the fundamental convergence theorems on the mean-square convergence orders of numerical approximations for a class of important backward stochastic differential equations (BSDEs) and for stochastic Schrödinger equation. The theorems show that the mean-square order of convergence of a numerical method for BSDEs depends on the properties of mean-square deviation of one-step approximation only, while the mean-square convergence order of a numerical method for stochastic Schrödinger equation depends on the properties of one-step approximation both in mean and mean-square sense, and on the estimate of semigroup operators.
Edited by: Guo Xinyu
Source: School of Mathematical Sciences