Non-densely defined impulsive neutral stochastic functional differential equations driven by fBm in Hilbert space with infinite delay

Abstract

We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion (fBm) with Hurst parameter H∈ (1/2, 1) in the Hilbert space. We prove the existence and uniqueness of the integral solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions. The results are obtained by using the method of successive approximation.

Keywords

Stochastic functional differential equation / non-densely defined operator / cylindrical fractional Brownian motion (fBm) / impulsive effect

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Higher Education Press and Springer-Verlag Berlin Heidelberg