随机微分方程数值解的几乎必然稳定区域  

Almost sure stability region of numerical scheme for stochastic differential equations

作　　者：郭海山[1] 胡良剑[1] 

机构地区：[1]东华大学应用数学系,上海200051

出　　处：《纺织高校基础科学学报》2010年第1期54-58,共5页Basic Sciences Journal of Textile Universities

摘　　要：从研究SDE数值解入手,证明了线性标量SDE的Euler-Maruyama方法数值解的几乎必然指数稳定的几个条件,并且找出了Euler-Maruyama方法数值解几乎必然指数稳定区域;通过与Saito和Mitsui研究的Euler-Maruyama方法数值解的均方稳定区域做比较,可以发现得到的几乎必然指数稳定区域更大,因此也是更有价值的.Starting from numerical stability,almost sure exponential stability conditions of the Euler-Maruyama method for linear scalar SDEs are proved, and the stability regions of numerical solution for linear scalar SDEs are identi-ed, By comparing with the mean-square stability regions reported by Saito and Mitsui,the almostsure stability regions in this paper is larger than the corresponding mean-square stability regions,andtherefore they are more valuable.

关 键 词：随机微分方程 Euler—Maruyama方法 数值解 几乎必然指数稳定 

分 类 号：O211.63[理学—概率论与数理统计]