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Successive approximation of neutral stochastic evolution equations with infinite delay and Poisson jumps. (English) Zbl 1248.34120

The authors consider a class of neutral stochastic evolution equations with infinite delay and Poisson jumps in real separable Hilbert spaces. They establish the existence and uniqueness of mild solutions under some kind of non-Lipschitz conditions. Also, they show the continuous dependence of the solutions on the initial data.
Reviewer: Yong Ren (Wuhu)

MSC:

34K50 Stochastic functional-differential equations
34K30 Functional-differential equations in abstract spaces
34K40 Neutral functional-differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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