Abstract and Applied Analysis
Volume 2012 (2012), Article ID 127397, 24 pages
http://dx.doi.org/10.1155/2012/127397
Research Article

Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions

Minghui Song and Hui Yu

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 3 April 2012; Accepted 22 May 2012

Academic Editor: Zhenya Yan

Copyright © 2012 Minghui Song and Hui Yu. 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

The Euler method is introduced for stochastic differential delay equations (SDDEs) with Poisson random measure under the generalized Khasminskii-type conditions which cover more classes of such equations than before. The main aims of this paper are to prove the existence of global solutions to such equations and then to investigate the convergence of the Euler method in probability under the generalized Khasminskii-type conditions. Numerical example is given to indicate our results.