报告人：Prof. Chuchu Chen (LSEC, AMSS)
地点：Room 1303, Sciences Building No. 1
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.