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**Stability of nonlinear neutral stochastic functional differential equations.**
*(English)*
Zbl 1206.60058

Summary: 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. The 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.

### MSC:

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

34K20 | Stability theory of functional-differential equations |

34K50 | Stochastic functional-differential equations |

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\textit{M. Xue} et al., J. Appl. Math. 2010, Article ID 425762, 26 p. (2010; Zbl 1206.60058)

### References:

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