Numerical Methods for Stochastic Differential Equations: part I

主讲人：Professor Xuerong Mao，University of Strathclyde

时间：2021年7月11日19:00

地点：腾讯会议 737 3753 2094

举办单位：数理学院

内容介绍：Up to 2002, all positive results on the numerical methods for SDEs were based on  a much more restrictive global Lipschitz assumption (namely both shift and  diffusion coefficients satisfy the global Lipschitz condition). However, the  global Lipschitz assumption rules out most realistic models. In 2002, Higham,  D.J., Mao, X. and Stuart, A.M. (SIAM Journal on Numerical Analysis 40(3) (2002),  1041-1063) were first to study the strong convergence of numerical solutions of  SDEs under a local Lipschitz condition. The field of numerical analysis of SDEs  now has a very active research profile, much of which builds on the techniques  developed in that paper, which has so far attracted 653 Google Scholar  Citations. In particular, the theory developed there has formed the foundation  for several recent very popular methods, including tamed Euler-Maruyama method  and truncated Euler-Maruyama. This summer SDE course will begin with Higham et  al 2002 but concentrate on the truncated Euler-Maruyama. The course will not  only discuss the finite-time strong convergence and its rates but also the  long-term properties including stability and boundedness. As an important  application, the course will develop new numercial schemes for the well-known  stochastic Lotka--Volterra model for interacting multi-species. We will show how  to modify the truncated Euler-Maruyama to establish a new positive preserving  truncated EM (PPTEM).