报告题目： Explicit Numerical Approximations for Stochastic Differential Equations in Finite and Infinite Horizons

报告人：李晓月教授（东北师范大学）

报告时间：2020年11月26日 10:00—12:00

报告地点：腾讯会议 299 958 091

报告摘要：Solving stochastic differential equations (SDEs) numerically, explicit Euler-Maruyama (EM) schemes are used most frequently under global Lipschitz conditions for both drift and diffusion coefficients. In contrast, without imposing the global Lipschitz conditions, implicit schemes are often used for SDEs but require additional computational effort; along another line, tamed EM schemes and truncated EM schemes have been developed recently. Taking advantages of being explicit and easily implementable, truncated EM schemes are proposed in this paper. Convergence of the numerical algorithms is studied, and $p$th moment boundedness is obtained. Furthermore, asymptotic properties of the numerical solutions such as the exponential stability in $p$th moment and stability in distribution are examined. Several examples are given to illustrate our findings.

报告人简介：李晓月，东北师范大学数学与统计学院教授，博士生导师。现任美国数学会评论员、国家自然科学基金委函评专家。长期从事随机微分方程稳定性理论、应用及数值逼近的研究, 发表SCI检索论文30余篇，单篇引用率达200余次，部分成果发表在SIAM J. Numer. Anal.、 SIAM J. Appl. Math.、IMA J. Numer. Anal.、J. Differential Equations 等学术期刊上。主持过国家自然科学基金项目和省部级项目多项。