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Abstract and Applied Analysis
Volume 2012, Article ID 371239, 20 pages
http://dx.doi.org/10.1155/2012/371239
Research Article

Existence and Uniqueness of Solutions to Neutral Stochastic Functional Differential Equations with Poisson Jumps

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2Department of Mechanics, Tianjin University, Tianjin 300072, China

Received 9 March 2012; Revised 12 May 2012; Accepted 15 May 2012

Academic Editor: Márcia Federson

Copyright © 2012 Jianguo Tan et al. 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

A class of neutral stochastic functional differential equations with Poisson jumps (NSFDEwPJs), d[x(t)-G(xt)]=f(xt, t)dt+g(xt,t)dW(t)+h(xt,t)dN(t), t[t0,T], with initial value xt0=ξ={ξ(θ):-τθ0}, is investigated. First, we consider the existence and uniqueness of solutions to NSFDEwPJs under the uniform Lipschitz condition, the linear growth condition, and the contractive mapping. Then, the uniform Lipschitz condition is replaced by the local Lipschitz condition, and the existence and uniqueness theorem for NSFDEwPJs is also derived.