主講人：Professor Xuerong Mao，University of Strathclyde
地點：騰訊會議 737 3753 2094
主講人介紹：英國思克萊德大學(University of Strathclyde)教授，愛丁堡皇家學會（即蘇格蘭皇家學院）院士。2015年度英國Leverhulme 研究獎，2016 年度英國皇家協會Wolfson 研究功勛獎。
內容介紹：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).