Transportation inequalities for coupled systems of stochastic delay evolution equations with a fractional Brownian motion

Abstract

We prove an existence and uniqueness result of mild solution for a system of stochastic semilinear differential equations with fractional Brownian motions and Hurst parameter H < 1/2. Our approach is based on Perov’s fixed point theorem, and we establish the transportation inequalities, with respect to the uniform distance, for the law of the mild solution.