主讲人简介：

Xuerong Mao received the Ph.D. degree from Warwick University, Coventry, U.K., in 1989. He was SERC (Science and Engineering Research Council, U.K.) Post-Doctoral Research Fellow from 1989 to 1992. Moving to Scotland, he joined the University of Strathclyde, Glasgow, U.K., as a Lecturer in 1992, was promoted to Reader in 1995, and was made Professor in 1998 which post he still holds. He was elected as a Fellow of the Royal Society of Edinburgh (FRSE) in 2008. He has authored five books and over 200 research papers. His main research interests lie in the field of stochastic analysis including stochastic stability, stabilization, control, numerical solutions, and stochastic modeling in finance, economic, and population systems.

内容摘要：

Influenced by Higham, Mao and Stuart (2002), several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations (SDEs) under the local Lipschitz condition. These numerical methods include the tamed Euler--Maruyama (EM) method, the tamed Milstein method, the stopped EM, the backward EM, the backward forward EM, etc. Recently, we developed a new explicit method in Mao (2015), called the truncated EM method, for the nonlinear SDE and established the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. However,we did not study the convergence rates for the method there,which is the aim of this paper. We will,under some additional conditions, discuss the rates of L^q-convergence of the truncated EM method for 2<q<p and show that the order of L^q-convergence can be arbitrarily close to q/2.

讲座主持：胡良剑 教授

讲座语言：英文