多维马尔科夫转制随机微分方程的数值解

摘要

由于多维马尔科夫转制随机微分方程不存在解析解，利用 Euler-Maruyama 方法给出多维马尔科夫转制随机微分方程的渐进数值解，并证明了此数值解收敛到方程的解析解。将单一马尔科夫转制随机微分方程的数值解问题延伸到多维马尔科夫转制情形，增强了马尔科夫转制随机微分方程的适用性。%Since stochastic differential equations with Multi-Markovian switching do not have explicit solutions, the Euler-Maruyama numerical solutions are obtained according to the Euler-Maruyama scheme. And it is proved that the approximate solutions will converge to the exact solutions. In this paper, the numerical theory of stochastic differential equations with single Markovian switching has been extended to the case of Multi-Markovian switching, which will lead to better applicability of stochastic differential equations with Markovian switching.