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

2025/06/19 by Ivkovic, Iván, Rásonyi, Miklós
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.16088

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.

Citations

• Regularization lemmas and convergence in total variation
• Non-asymptotic bounds for sampling algorithms without log-concavity
• Quantitative contraction rates for Markov chains on general state spaces
• Quantitative Harris type theorems for diffusions and McKean-Vlasov\n processes
• Yet another look at Harris' ergodic theorem for Markov chains

Related

• Rate estimates for total variation distance with applications
• Wasserstein and total variation distance between marginals of L 'evy\n processes
• The Breuer-Major Theorem in total variation: improved rates under\n minimal regularity
• Mean convergence rates for Gaussian-smoothed Wasserstein distances and classical Wasserstein distances
• Total variation estimates in the Breuer-Major theorem