Convergence Rate of the Truncated Euler-Maruyama Method for Neutral Stochastic Differential Delay Equations with Markovian Switching

Abstract

The key aim of this paper is to show the strong convergence of the truncated Euler-Maruyama method for neutral stochastic differential delay equations (NSDDEs) with Markovian switching (MS) without the linear growth condition. We present the truncated Euler-Maruyama method of NSDDEs-MS and consider its moment boundedness under the local Lipschitz condition plus Khasminskii-type condition. We also study its strong convergence rates at time $T$ and over a finite interval $[0, T]$. Some numerical examples are given to illustrate the theoretical results.