Rate estimates for weighted total variation norm in terms of Wasserstein distances

TL;DR

This paper establishes estimates for weighted total variation distances between probability measures using Wasserstein distances, leveraging Fourier analysis and applying results to Malliavin calculus convergence.

Contribution

It introduces new bounds relating weighted total variation and Wasserstein distances under smoothness and moment conditions, with applications to Malliavin calculus.

Findings

Derived bounds connecting total variation and Wasserstein distances

Applied estimates to convergence problems in Malliavin calculus

Utilized Fourier-analytic techniques for probability measure analysis

Abstract

We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment conditions. We apply our results to convergence of functionals in Malliavin calculus.