Journal of Applied Mathematics
Volume 2012 (2012), Article ID 305945, 14 pages
http://dx.doi.org/10.1155/2012/305945
Research Article

Analytic Approximation of the Solutions of Stochastic Differential Delay Equations with Poisson Jump and Markovian Switching

Hua Yang1 and Feng Jiang2

1School of Mathematics and Computer, Wuhan Polytechnic University, Wuhan 430023, China
2School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China

Received 2 May 2011; Revised 2 July 2011; Accepted 5 July 2011

Academic Editor: Ying U. Hu

Copyright © 2012 Hua Yang and Feng Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We are concerned with the stochastic differential delay equations with Poisson jump and Markovian switching (SDDEsPJMSs). Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEsPJMSs when the drift and diffusion coefficients are Taylor approximations.