一、题目: Explicit Approximations for Stochastic Differential Equations in Finite and Infinite Horizons
二、主讲人：李晓月
三、时 间：2019年6月8日（周六），下午：15：45-16：25
四、地 点：闻理园A4-218室
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, 博导；近些年来主要从事随机微分方程稳定性理论以及数值逼近方面的研究，成果发表在 JDE，SIAM，J. Num. Anal., Automatica 等多个国际杂志上；曾主持国际自然科学基金面上项目，国家自然科学基金青年项目，参与了多项国家自然科学基金和教育部项目的研究工作；2007年11月-2008年11月访问英国斯特莱斯克莱德大学；2014年11月-2015年11月访问美国韦恩州立大学；现为 Mathematical Review以及多个杂志的审稿人。
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理学院非线性分析研究所
2019年6月3日
