Abstract
We consider modified Zolotarev’s ideal metrics for probability distri¬butions on the real line and explore their connections with Lévy’s, total variation, and transport distances. In particular, E. Rio’s upper bound on the power trans¬port (Kantorovich) distances is reversed under (necessary) moment assumptions and is sharpened for compactly supported measures. We also explain the role of such metrics in the study of the central limit theorem.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1207-1228 |
| Number of pages | 22 |
| Journal | Pure and Applied Functional Analysis |
| Volume | 10 |
| Issue number | 5 |
| State | Published - 2025 |
Bibliographical note
Publisher Copyright:© Copyright 2025.
Keywords
- Zolotarev ideal metrics
- transport inequalities
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