  This work deals with the Euler-Maruyama (EM) scheme for stochastic
differential equations with Markovian switching (SDEwMSs). We focus on the
Lp-convergence rate (p is greater than or equal to 2) of the EM method given in
this paper. As far as we know, the skeleton process of the Markov chain is used
in the continuous numerical methods in most papers. By contrast, the continuous
EM method in this paper is to use the Markov chain directly. To the best of our
knowledge, 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 EM
method can reach 1/2. We believe that the technique used in this paper to
construct the EM method can also be used to construct other methods for
SDEwMSs.
