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Razumikhin-type theorems on exponential stability of stochastic functional differential equations with infinite delay. (English) Zbl 1198.34182

Summary: 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 \(p\)th moment and almost sure exponential stability. Finally, some examples are presented to illustrate our theory.

MSC:

34K50 Stochastic functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K20 Stability theory of functional-differential equations
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