Strong convergence of the balanced Euler method for neutral stochastic differential delay equations with Markovian switching

Abstract

In this paper, the strong convergence of the balanced Euler method for neutral stochastic differential delay equations with Markovian switching (NSDDEs-MS) without the linear growth condition is concerned. We present the balanced Euler method of NSDDEs-MS and consider its moment boundedness under polynomial growth condition plus Khasminskii-type condition. We also study its strong convergence order. A numerical example is given to support the theoretical results.