主讲人：Professor Xuerong Mao，University of Strathclyde
地点：腾讯会议 737 3753 2094
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).