Stability of the split-step backward Euler scheme for stochastic delay integro-differential equations with Markovian switching

In this paper, we concentrate on the numerical approximation of solutions of stochastic delay integro-differential equations with Markovian switching (SDIDEsMS). We establish the split-step backward Euler (SSBE) scheme for solving linear SDIDEsMS and discuss its convergence and stability. Moreover, the SSBE method is convergent with strong order γ = 1/2 in the mean-square sense. The conditions under which the SSBE method is mean-square stable and general mean-square stable are obtained. Some illustrative numerical examples are presented to demonstrate the stability of the numerical method and show that SSBE method is superior to Euler method.