Stability analysis of neutral stochastic delay differential equations via the vector Lyapunov function method

Abstract

In this paper, we study the pth moment exponential stability (p-ES) and the almost sure exponential stability (a-ES) of neutral stochastic delay differential equations (NSDDEs). By using the vector Lyapunov function (VLF) method, we can prove that the global solution of NSDDEs exists when the linear growth condition is removed, and we also get some stability criteria for NSDDEs. In the presented stability conditions, the established L-operator differential inequality is based on the VLF and allows cross item to exist. An example is given to verify the correctness of the proposed results.