一、题目

Monte Carlo Simulations of SDE Models

二、主讲人

Xuerong Mao

三、摘要

Most of SDE models in epidemics, ecology, biology, finance etc. are highly nonlinear and do not have explicit solutions. Monte Carlo simulations have played a more and more important role. This talk will point out several well-known numerical schemes may fail to preserve the positivity or moment of the solutions to SDE models. Reliable numerical schemes are therefore required to be designed so that the corresponding Monte Carlo simulations can be trusted. The talk will then concentrate on new numercial schemes for the well-known stochastic Lotka--Volterra model for interacting multi-species. This model has some typical features: highly nonlinear, positive solution and multi-dimensional. The known numerical methods including the tamed/truncated Euler-Maruyama (EM) applied to it do not preserve its positivity. The aim of this talk is to modify the truncated EM to establish a new positive preserving truncated EM (PPTEM).

四、主讲人介绍

毛学荣教授是英国斯克莱德大学数学与统计系教授、英国苏格兰皇家学院院士。也是“英国沃弗森研究功勋奖”获得者。国际知名的随机稳定性和随机控制领域的专家；擅长随机分析，在对随机系统处理方面，提出了系列处理方法与技巧，被广泛采用。例如，对噪声镇定给出了科学的理论，被后续跟踪者所广泛推崇；在随机人口理论方面作出了贡献；在随机系统LaSalle原理方面作出了开拓性的工作；奠定了随机跳变系统理论方面的研究。目前他引领着对高非线性随机系统的稳定，镇定，数值计算与仿真的研究。至今，已出版学术专著五部，在国际学术杂志上发表了许多高影响的论文。被SCI收录论文309篇，引用13086次，H指数62。

五、邀请人

陈章 数学学院教授

六、时间

12月3日（周五）20:00-21:00

七、地点

腾讯会议，会议ID：788 558 384

八、主办方

山东大学数学学院