随机微分方程分步单支theta方法的稳定性(英文)  

Stability of Split-step One-leg Theta Methods for Stochastic Differential Equations

作　　者：李启勇[1,2] 甘四清[2] 

机构地区：[1]怀化学院数学系,湖南怀化418008 [2]中南大学数与计算技术学院,湖南长沙410075

出　　处：《应用数学》2012年第1期209-213,共5页Mathematica Applicata

基　　金：Supported by the NSF of China(10871207);the Hunan Provincial Innovation Foundation for Postgraduates(CX2010B118)

摘　　要：本文研究随机微分方程单支theta方法的均方稳定性.首先,对线性检验方程,当0≤θ<1时,分步单支theta方法在一定的步长限制下能保持原系统的均方稳定性,当θ=1时,方法按任意步长都能保持原系统的稳定性.其次,对满足单边Lipschitz条件的非线性随机微分方程,当1/2<θ0<θ<1时,方法能保持原系统的均方指数稳定性,但对步长有限制,如果θ=1,对步长限制消失.In this paper,we are concerned with the mean-square stability properties of split-step one-leg theta methods for stochastic differential equations（SDEs）.First,for a linear scalar test problem,the method with 0≤θ1 preserves the mean-square stability of the test equation,but with a stepsize restriction,while the method with θ=1 well preserve the stability property without any constraints on the stepsize.Second,for nonlinear SDEs that have a negative one-sided Lipschitz constant,the method with 1/2θ0θ1 can reproduce exponential mean-square stability properties under a restriction on stepsize.In the case θ=1,the restriction on stepsize disappears.

关 键 词：分步单支theta方法 单边LIPSCHITZ条件 均方稳定 非线性稳定 

分 类 号：O211.63[理学—概率论与数理统计]