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Journal of Applied Mathematics
Volume 2012, Article ID 675781, 17 pages
http://dx.doi.org/10.1155/2012/675781
Research Article

Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients

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

Received 15 January 2012; Revised 20 March 2012; Accepted 22 March 2012

Academic Editor: Said Abbasbandy

Copyright © 2012 Hui Yu and Minghui Song. 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 numerical methods in the current known literature require the stochastic differential equations (SDEs) driven by Poisson random measure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler's method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. The main aim is to investigate the convergence of the Euler method in probability to such equations with non-Lipschitz coefficients. Numerical example is given to demonstrate our results.