Journal of Applied Mathematics
Volume 2010 (2010), Article ID 425762, 26 pages
doi:10.1155/2010/425762
Research Article

Stability of Nonlinear Neutral Stochastic Functional Differential Equations

Minggao Xue,1 Shaobo Zhou,2 and Shigeng Hu2

1School of Management, Huazhong University of Science and Technology, Wuhan 430074, China
2School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

Received 17 June 2010; Revised 14 September 2010; Accepted 18 September 2010

Academic Editor: Neville Ford

Copyright © 2010 Minggao Xue 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

Neutral stochastic functional differential equations (NSFDEs) have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper is to remove the linear growth condition and establish a Khasminskii-type test for nonlinear NSFDEs. New criteria not only cover a wide class of highly nonlinear NSFDEs but they can also be verified much more easily than the classical criteria. Finally, several examples are given to illustrate main results.