New criteria on asymptotic behavior of neutral stochastic functional differential equations

This paper investigates the asymptotic behavior of neutral stochastic functional differential equations (NSFDEs) under both the local Lipschitz condition and the one dependent on the diffusion operator and on a coercivity term, which is more general than the classical growth condition. Some sufficient conditions for stability with general decay rate and boundedness of NSFDEs are derived via the Lyapunov analysis method and some stochastic analysis techniques. Our results not only cover a wide class of highly nonlinear NSFDEs but they can also deal with general stability issues including the polynomial stability and the exponential stability. Finally, an illustrative example is provided to show the effectiveness of our theoretical results.