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Stochastic functional differential equations with infinite delay. (English) Zbl 1173.60331

Authors’ abstract: The stability and boundedness of the solution for stochastic functional differential equation with finite delay have been studied by several authors, but there is almost no work on the stability of the solutions for stochastic functional differential equations with infinite delay. The main aim of this paper is to close this gap. We establish criteria of \(p\)th moment \(\psi ^{\gamma }(t)\)-bounded for neutral stochastic functional differential equations with infinite delay and exponentially stable criteria for stochastic functional differential equations with infinite delay, and we also illustrate the result with an example.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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