| 多维马尔科夫转制随机微分方程的数值解 |
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| 引用本文： | 耿晓晶. 多维马尔科夫转制随机微分方程的数值解[J]. 纯粹数学与应用数学, 2013, 0(6): 646-653 |
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| 作者姓名： | 耿晓晶 |
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| 作者单位： | 暨南大学经济学院统计学系,广东广州510632 |
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| 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．
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| 关 键 词： | 多维马尔科夫转制随机微分方程 Euler—Maruyama数值解 收敛性 |
Numerical solutions of stochastic differential equations with Multi-Markovian switching |
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| Geng Xiaojing. Numerical solutions of stochastic differential equations with Multi-Markovian switching[J]. Pure and Applied Mathematics, 2013, 0(6): 646-653 |
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| Authors: | Geng Xiaojing |
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| Affiliation: | Geng Xiaojing (Department of Statistics, Ji＇nan University, Guangzhou 510632, China) |
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| Abstract: | 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 Maxkovian switching. |
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| Keywords: | SDEs with Multi-Markovian switching Euler-Maruyama scheme convergence |
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