Wasserstein upper bounds of Lp-norms for multivariate densities in Besov spaces

Minwoo Chae

Statistics & Probability Letters, 2024, vol. 210, issue C

Abstract: While the total variation between two probability measures cannot be bounded by Wasserstein metrics in general, it is possible if they possess smooth densities. More generally, we demonstrate that Lp-distances between densities in Besov spaces can be bounded by powers of the Wasserstein metrics.

Keywords: Besov space; Metric inequality; Probability metric; Total variation; Wasserstein metric (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110131

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