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

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.