报告人：毛学荣

时间：8月7日(周一)下午14:00-15:30

地点：2号学院楼235

主讲人简介：英国思克莱德大学教授

报告摘要：

This work develops a novel approximation for a class of superlinear stochastic Kolmogorov equations with positive global solutions. On the one hand, most existing explicit methods that work for the superlinear stochastic differential equations (SDEs), e.g. various modified Euler-Maruyama (EM) methods, fail to preserve positivity of the solution. On the other hand, methods that preserve positivity are mostly implicit, or fail to cope with the multi-dimensional scenario. This work aims to construct an advanced numerical method which is not only naturally structure preserving but also cost effective. A strong convergence framework is then developed with an almost optimal convergence rate of order arbitrarily close to $1/2$. To make the arguments concise, we elaborate our theory with the generalised stochastic Lotka-Volterra model, though the method is applicable to a wide bunch of multi-dimensional superlinear stochastic Kolmogorov systems in various fields including finance and epidemiology. 

主持人：胡良剑