Positivity and lower bounds for the density of Wiener functionals

Abstract

We consider a functional on the Wiener space which is smooth and not degenerated in Malliavin sense and we give a criterion of strict positivity of the density. We also give lower bounds for the density. These results are based on the representation of the density by means of the Riesz transform introduced by Malliavin and Thalmaier and on the estimates of the Riesz transform given Bally and Caramellino.