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This work deals with the Euler-Maruyama (EM) scheme for stochasticdifferential equations with Markovian switching (SDEwMSs). We focus on theLp-convergence rate (p is greater than or equal to 2) of the EM method given inthis paper. As far as we know, the skeleton process of the Markov chain is usedin the continuous numerical methods in most papers. By contrast, the continuousEM method in this paper is to use the Markov chain directly. To the best of ourknowledge, there are only two papers that consider the rate of Lp-convergence,which is no more than 1/p (p is greater than or equal to 2) in these papers.The contribution of this paper is that the rate of Lp-convergence of the EMmethod can reach 1/2. We believe that the technique used in this paper toconstruct the EM method can also be used to construct other methods forSDEwMSs.

The rate of Lp-convergence for the Euler-Maruyama method of the stochastic differential equations with Markovian switching