MS-stability of the Euler–Maruyama method for stochastic differential delay equations

摘要

The aim of this paper is to investigate the stability of the Euler–Maruyama method for the stochastic differential equations with time delay. The definition of MS-stability of numerical methods is established. The condition of the mean square stability of analytical solution is obtained for a linear scalar system with multiplicative noise, and the MS-stability of the numerical scheme is proved.