Concentration inequalities via Malliavin calculus with applications

Concentration inequalities via Malliavin calculus with applications

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 ...

Density formula and concentration inequalities with Malliavin calculus

We show how to use the Malliavin calculus to obtain a new exact formula for the density ρ of the law of any random variable Z which is measurable and di erentiable with respect to a given isonormal Gaussian process. The main advantage of this formula is that it does not refer to the divergence operator (dual of the Malliavin derivative). In particular, density lower bounds can be obtained in so...

Density estimates and concentration inequalities with Malliavin calculus

We show how to use the Malliavin calculus to obtain density estimates of the law of general centered random variables. In particular, under a non-degeneracy condition, we prove and use a new formula for the density ρ of a random variable Z which is measurable and di erentiable with respect to a given isonormal Gaussian process. Among other results, we apply our techniques to bound the density o...

Malliavin calculus and its applications

Chapter Vi - the Malliavin Calculus and Applications