Mean square stability of semi-implicit Euler method for linear stochastic differential equations with multiple delays and Markovian switching

In this paper, we study the mean square (MS) stability and general mean square (GMS) stability of semi-implicit Euler method for linear stochastic differential equations with multiple delays and Markovian switching. It is proved that semi-implicit Euler method is MS-stable and GMS-stable under suitable conditions. A numerical example is provided to illustrate the theoretical results.