Explicit Approximations for Nonlinear Stochastic Systems
报 告 人:: 李晓月
报告地点:: 数学与统计学院二楼会议室
报告时间:: 2017年12月15日星期五15:10-15:50

To approximate solutions of stochastic differential equations (SDEs), explicit Euler-Maruyama (EM) schemes have been used most frequently under global Lipschitz conditions for both drift and diffusion coefficients, whereas implicit schemes have been used widely for SDEs without this condition but require additional computational effort for the implementation. In addition, tamed EM schemes and the truncated EM schemes have recently been developed for SDEs without satisfying the global Lipschitz condition. Taking advantages of being explicit and easily implementable, modified and truncated EM schemes are proposed in this paper. It is shown that our modified truncated EM schemes preserve the asymptotic pth moment boundedness of the underlying SDEs. Furthermore, different schemes are constructed to approximate the dynamical behaviors such as the exponential stability in pth moment and stability in distribution. Several examples are given to illustrate our findings.

发 布 人:科研助理 发布时间: 2017-12-13
李晓月,东北师范大学数学与统计学院教授,主要从事随机微分方程稳定性理论及其应用问题、逼近理论方面的研究。主持了国际自然科学基金面上项目,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。