Positivity and lower bounds for the density of Wiener functionals

TL;DR

This paper establishes criteria for the strict positivity and lower bounds of densities of Wiener functionals using Malliavin calculus and Riesz transform techniques, advancing understanding of their probabilistic properties.

Contribution

It introduces new criteria for positivity and lower bounds of Wiener functional densities based on Malliavin calculus and Riesz transform estimates.

Findings

Criteria for strict positivity of Wiener functional densities

Lower bounds for the densities of Wiener functionals

Application of Riesz transform estimates to density analysis

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.