Transportation Inequalities for Neutral Stochastic Differential Equations Driven by Fractional Brownian Motion with Hurst Parameter Lesser Than 1/2

Abstract

In this note, we prove an existence and uniqueness result of mild solution for a neutral stochastic differential equation with finite delay, driven by a fractional Brownian motion with Hurst parameter lesser than 1/2 in a Hilbert space, and we establish the transportation inequalities, with respect to the uniform distance, for the law of the mild solution.