线性分段连续型随机微分方程数值解的收敛性和稳定性

Convergence and Stability of Numerical Solutions for Linear Stochastic Differential Equations with Piecewise Continuous Arguments

把Back-Euler方法应用到线性分段连续型随机微分方程上,研究对给定步长该方程数值解的收敛性和对任意步长数值解的均方稳定性,在处理线性项的矩阵时,证明的方法主要应用了矩阵范数,从而达到要研究线性分段连续型随机微分方程数值解的收敛性和稳定性的目的.

In this paper, applying the Back -Euler method to linear stochastic differential equations with piecewise continuous arguments. The convergence of numerical solutions of the equation for given step size and stability in mean square of numerical solutions for any step size are studied. We base on definition of matrix norm in the linear matrix term. In order to study convergence and stability of semi - linear stochastic differential equations with piecewise continuous arguments.