Numerical Solution of Nonlinear Stochastic Differential Delay Equation with Markovian Switching

Chaozhu Hu^1, and Shaobo Zhou²

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

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

Cite this paper:
Chaozhu Hu and 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

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.

Keywords:
stochastic differential delay equation Euler-Maruyama convergence in probability markovian switching

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