Impulsive stochastic functional differential equations with Markovian switching: study of exponential stability from a numerical solution point of view

Abstract This paper is devoted to the study of stochastic functional differential systems with Markov switching. It focuses on the stability of numerical solutions. To gain insight on how impulses, functional past dependence, random switching and stochastic disturbances can have impact on dynamic systems, this paper addresses exponential stability of the Euler–Maruyama approximations of stochastic functional differential equations with impulsive perturbations and Markovian switching. It begins with a presentation of the definitions of exponential stability in mean square and in the almost sure sense for stochastic functional differential equations with impulsive perturbations and Markovian switching. Then, it is devoted to showing that if the underlying system is stable in the aforementioned sense then the Euler–Maruyama approximation method faithfully reproduces exponential stability in the mean square and almost sure sense for sufficiently small step sizes and large iteration number. Two examples are provided to demonstrate the effectiveness of our results.