单调型条件下随机微分方程θ-方法的均方指数稳定性(英文)  

Moment Exponential Stability of the θ-method for Stochastic Differential Equations with Monotone-type Condition

作　　者：陈琳[1] 殷荣城[1] 

机构地区：[1]华中科技大学数学与统计学院,湖北武汉430074

出　　处：《应用数学》2013年第1期228-235,共8页Mathematica Applicata

摘　　要：本文研究高度非线性随机微分方程(SDEs)的数值解稳定性性质.给出θ-方法均方指数稳定性的充分条件.与现有文献不同,本文无需单边线性增长条件和充分小的步长.本文在单调型的条件下,并且至于要步长满足一个很弱的条件即可.因此本文是对现有文献的很大改进.This paper deals with numerical stability properties of highly nonlinear stochastic differ- ential equations （SDEs）. Sufficient conditions for moment exponential stability of theθ-methods are investigated. Different from existing literature, in this paper, we do not need one-side linear growth condition and sufficient small step size. We consider the monotone condition,and only a very weak restriction of the step size. This improves the existing results greatly.

关 键 词：随机微分方程 均方指数稳定性 Θ-方法 单调条件 

分 类 号：O211.63[理学—概率论与数理统计]