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

摘要

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.