应用数学2012，Vol.25Issue(1)：209-213,5.
随机微分方程分步单支theta方法的稳定性
Stability of Split-step One-leg Theta Methods for Stochastic Differential Equations
摘要
Abstract
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 ≤ θ＜ 1 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 1/2 ＜ θo ＜ θ ＜ 1 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Key words
Split-step one-leg theta methods/One-sided Lipschitz condition/Mean square stability/Nonlinear stability分类
数理科学引用本文复制引用
李启勇,甘四清..随机微分方程分步单支theta方法的稳定性[J].应用数学,2012,25(1):209-213,5.基金项目
Supported by the NSF of China(10871207) and the Hunan Provincial Innovation Foundation for Postgraduates(CX2010B118) （10871207）
