Mean-square stability of analytic solution and Euler–Maruyama method for impulsive stochastic differential equations

From the view of algebra, the mean-square stability of analytic solutions and numerical solutions for impulsive stochastic differential equations are considered. By the logarithmic norm, the conditions under which the analytic and numerical solutions for a linear impulsive stochastic differential equation are mean-square stable (MS-stable) respectively are obtained. The conditions are simple and easy to use. Some numerical experiments are given to illustrate the results.