Exponential Stability of Highly Nonlinear Neutral Stochastic Differential Delay Equations

This paper investigates the mean square and almost sure stability of a class of neutral stochastic differential delay equations with highly nonlinear coefficients. We first examine the regularity of the solution to the highly nonlinear neutral stochastic differential delay systems. Then the explicit stability conditions are obtained by the Lyapunov functional and semi-martingale convergence theorem. Especially, the explicit stability conditions of pure delay neutral stochastic differential delay equations are obtained. It is revealed that the delay term in the drift can contribute to the mean square and almost sure stability.