Solving the stochastic differential systems with modified split-step Euler-Maruyama method

Abstract

A new category of the split-step Euler-Maruyama types schemes are constructed to study the stochastic differential systems. Under given conditions, we analyze the mean-square convergence in the strong sense. Also, for two class of Itô test systems, we investigate the asymptotic mean-square stability. Finally, several linear and nonlinear applied test problems are considered to confirm the theoretical results.