Stochastic stability of a class of unbounded delay neutral stochastic differential equations with general decay rate

Abstract

Without the linear growth condition on the drift coefficient, this article examines the existence and uniqueness of global solutions of a class of neutral stochastic differential equations with unbounded delay and their asymptotic stabilities with general decay rate. To illustrate the application of our results, this article gives a two-dimensional system as an example.

Keywords:

• ψ-type stability
• global solutions
• neutral stochastic differential equations
• unbounded delay

Acknowledgements

The authors thank the referees for their detailed comments and helpful suggestions. The financial support from the National Natural Science Foundation of China (Grant No. 10971077) is gratefully acknowledged.