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The main aim of this paper is to study the stability of the stochastic functional differential equations with infinite delay. We establish several Razumikhin-type theorems on the exponential stability for stochastic functional differential equations with infinite delay. By applying these results to stochastic differential equations with distributed delay, we obtain some sufficient conditions for both pth moment and almost surely exponentially stable. Finally, some examples are presented to illustrate our theory.

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The pth moment exponential stability of stochastic Cohen-Grossberg with time-varying delays is investigated in this paper. A set of novel sufficient conditions on pth moment exponential stability are given for the considered system by using the wellknown Razumikhin-type theorem. Finally, two examples with their numerical simulations are provided to show the correctness of our analysis.

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