Open Access
2010 Stability of Nonlinear Neutral Stochastic Functional Differential Equations
Minggao Xue, Shaobo Zhou, Shigeng Hu
J. Appl. Math. 2010: 1-26 (2010). DOI: 10.1155/2010/425762


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.


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Minggao Xue. Shaobo Zhou. Shigeng Hu. "Stability of Nonlinear Neutral Stochastic Functional Differential Equations." J. Appl. Math. 2010 1 - 26, 2010.


Published: 2010
First available in Project Euclid: 12 August 2011

zbMATH: 1206.60058
MathSciNet: MR2735304
Digital Object Identifier: 10.1155/2010/425762

Rights: Copyright © 2010 Hindawi

Vol.2010 • 2010
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