Convergence and stability of numerical solutions to SDDEs with Markovian switching

摘要

A class of linear stochastic delay differential equations with Markovian switching is considered. The main aim of this paper is to investigate the convergence and stability of the Euler method of the equations. It is proved that the Euler method is convergent with strong order p = 1/2. The MS-stable properties of the Euler scheme are also studied.