Mean square asymptotic stability of stochastic delayed systems by fixed point theory

In this paper, we consider a nonlinear neutral stochastic system with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory. These conditions do not require the roundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotically mean square stable theorem with necessary and sufficient condition is proved. Some results are improved and generalized.