分段连续型随机微分方程指数Euler方法的稳定性  

Stability of Exponential Euler Method for Linear Stochastic Differential Equations with Piecewise Continuous Arguments

作　　者：张玲 刘国清 邬德林[2] 李唐海 ZHANG Ling;LIU Guo-qing;WU De-lin;LI Tang-hai(Mathematical Department of Teacher Education Institute,Daqing Normal University,Daqing 163712,China;School of Economic Management,Daqing Normal University,Daqing 163712,China)

机构地区：[1]大庆师范学院教师教育学院数学系,大庆163712 [2]大庆师范学院经济管理学院,大庆163712

出　　处：《数学的实践与认识》2021年第1期295-301,共7页Mathematics in Practice and Theory

基　　金：黑龙江省自然科学基金联合引导项目(JJ2019LH2453);黑龙江省自然科学基金青年项目(QC2016001)。

摘　　要：给出了线性分段连续型随机微分方程指数Euler方法的均方指数稳定性.经典的对稳定性理论分析,通常应用的是Lyapunov泛函理论,然而,应用该方程本身的特点和矩阵范数的定义给出了该方程精确解的均方稳定性.以往对于该方程应用隐式Euler方法得到对于任意步长数值解的均方稳定性,而应用显式Euler方法得到了相同的结果.最后,给出实例验证结论的有效性.In this paper,exponential stability in mean square of the exponential Euler method to linear stochastic differential equation with piecewise continuous arguments is showed.In the classical analysis of stability theory,Lyapunov functional theory is usually used.However,in this paper,the mean square stability of the exact solution to the equation is given by using the characteristics of the equation itself and the definition of the matrix norm.In the past,the implicit Euler method was used to obtain the mean square stability of the numerical solution for the equation with arbitrary step size.The same result is obtained by using explicit Euler method in this paper.Finally,an example is given to verify the validity of the conclusion.

关 键 词：分段连续型随机微分方程 指数Euler方法 It?公式 均方稳定 

分 类 号：O211.63[理学—概率论与数理统计]