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Khasminskii-type theorems for stochastic functional differential equations with infinite delay. (English) Zbl 1230.34069

Summary: The classical Khasminskii-type theorem gives a powerful tool to examine the global existence of solutions for stochastic differential equations without linear growth condition by the use of Lyapunov functions. However, there is no such result for stochastic functional equations with infinite delay. The main aim of this paper is to establish existence-and-uniqueness theorems for global solutions to stochastic functional differential equations with infinite delay.

MSC:

34K50 Stochastic functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:

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