Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space

In this note we prove an existence and uniqueness result of mild solutions for a neutral stochastic differential equation with finite delay, driven by a fractional Brownian motion in a Hilbert space and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution. (c) 2012 Elsevier B.V. All rights reserved.