半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 semi-linear stochastic differential equations with piecewise continuous arguments

将Back-Euler方法应用到半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,在处理半线性项的矩阵时,证明的方法主要应用了矩阵范数,从而达到要研究半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。

Applying the Back-Euler method to semi-linear stochastic differential equations with piecewise continuous arguments, the convergence of numerical solutions of the equation for given step size and sta- bility in mean square of numerical solutions for any step size is studied. Definition of matrix norm is ap- plied to handle with the semi-linear matrix term. Thereby, convergence and stability of semi-linear sto- chastic differential equations with piecewise continuous arguments are studied.