Mean square exponential stability of stochastic nonlinear delay systems

In this paper, we are concernedwith the stability of stochastic nonlinear delay systems. Different from the previous literature, we aim to show that when the determinate nonlinear delay system is globally exponentially stable, the corresponding stochastic nonlinear delay system can be mean square globally exponentially stable. In particular, we remove the linear growth condition and introduce a new polynomial growth condition for g(x(t), x(t-tau(t))), which overcomes the limitation of application scope and the boundedness of diffusion term form. Finally, we provide an example to illustrate our results.