论文标题
Markovian Switching的随机微分方程的Euler-Maruyama方法的LP连接率
The rate of Lp-convergence for the Euler-Maruyama method of the stochastic differential equations with Markovian switching
论文作者
论文摘要
这项工作涉及Markovian Switching（SDEWMSS）的随机微分方程的Euler-Maruyama（EM）方案。我们关注本文给出的EM方法的LP连接率（P大于或等于2）。据我们所知，在大多数论文中，马尔可夫链的骨骼过程用于连续数值方法。相比之下，本文中的连续EM方法是直接使用马尔可夫链。据我们所知，只有两篇论文考虑了LP-Convergence的速率，这些论文不超过1/P（P大于或等于2）。本文的贡献是，EM方法的LP连接率可以达到1/2。我们认为，本文用于构建EM方法的技术也可以用于构建SDEWMSS的其他方法。
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.
