Concentration inequalities via Malliavin calculus with applications

Abstract

We use the Malliavin calculus to prove a new abstract concentration inequality result for zero mean, Malliavin differentiable random variables which admit densities. We demonstrate the applicability of the result by deriving two new concrete concentration inequalities, one relating to an integral functional of a fractional Brownian motion process, and the other relating to the centered maximum of a finite sum of Normal random variables. These concentration inequalities are, to the best of our knowledge, largely unattainable via existing methods other than those which are the subject of this paper.