Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion

Abstract

We establish Talagrand’s T₁ and T₂ inequalities for the law of the solution of a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H > 1/2. We use the L² metric and the uniform metric on the path space of continuous functions on [0, T]. These results are applied to study small-time and large-time asymptotics for the solutions of such equations by means of a Hoeffding-type inequality.