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.
翻译：这项工作涉及以 Markovian 转换 (SDEwMSs) 进行随机差分方程的 Euler- Maruyama (EM) 方案。 我们侧重于本文中给出的 EM 方法的 Lp- convergence 率( p 是大于或等于 2) 。 据我们所知, 多数文件中的连续数字方法使用了 Markov 链的骨架过程。 相反, 本文中持续的 EM 方法是直接使用 Markov 链 。 据我们所知, 只有两份文件考虑了 Lp- convergence 率, 这两份文件的 Lp- convergence 率不超过 1/p( p 是大于或等于 2) 。 本文的贡献是 EM 方法的 Lp- converggence 率可以达到 1/ /2 。 我们相信, 本文中用于构建 EM 方法的技术也可以用来为 SDEwMS 构建其他方法 。
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