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X. Mao, Stochastic Differential Equations and its Application, Horwood, 1997.

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Article

Numerical Solution of Nonlinear Stochastic Differential Delay Equation with Markovian Switching

1School of Science, Hubei University of Technology, Wuhan 430068, Hubei, China

2School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China


Journal of Mathematical Sciences and Applications. 2016, Vol. 4 No. 1, 20-28
DOI: 10.12691/jmsa-4-1-4
Copyright © 2016 Science and Education Publishing

Cite this paper:
Chaozhu Hu, Shaobo Zhou. Numerical Solution of Nonlinear Stochastic Differential Delay Equation with Markovian Switching. Journal of Mathematical Sciences and Applications. 2016; 4(1):20-28. doi: 10.12691/jmsa-4-1-4.

Correspondence to: Chaozhu  Hu, School of Science, Hubei University of Technology, Wuhan 430068, Hubei, China. Email: huchaozhu@126.cn

Abstract

This paper is concerned with the Euler-Maruyama approximate solution of nonlinear stochastic delay differential equations with Markovian switching (SDDEwMSs). We establish the existence and uniqueness results for the global solution of SDDEwMSs under the polynomial growth and the local Lipschitz condition. we then introduce Euler-Maruyama approximate solution of this equation, and establish the convergence in probability of the numerical solution to the exact solution of the problem without the linear growth condition. As an application, we also give one example to demonstrate our results.

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