Numerical solutions of stochastic functional differential equations with impulsive perturbations and Markovian switching

Abstract

This paper is focused on analysis of Euler–Maruyama-type approximations for stochastic functional differential equations with impulsive perturbations and Markovian switching. The motivation stems from a wide range of applications. The paper establishes mean square convergence of the approximations under a local Lipschitz condition and a linear growth condition. In addition, this work ascertains the rates of convergence of the numerical solutions under the global Lipschitz condition. Finally, the performance of the algorithm is demonstrated through a numerical example.