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In this note we consider a class of neutral stochastic functionaldifferential equations with finite delay driven simultaneously by a fractionalBrownian motion and a Poisson point processes in a Hilbert space. We prove anexistence and uniqueness result and we establish some conditions ensuring theexponential decay to zero in mean square for the mild solution by means of theBanach fixed point principle.

Neutral stochastic functional differential equation driven by fractional Brownian motion and Poisson point processes