Wasserstein upper bounds of \(L^p\)-norms for multivariate densities in Besov spaces (Q6569457)
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scientific article; zbMATH DE number 7878535
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Wasserstein upper bounds of \(L^p\)-norms for multivariate densities in Besov spaces |
scientific article; zbMATH DE number 7878535 |
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Wasserstein upper bounds of \(L^p\)-norms for multivariate densities in Besov spaces (English)
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9 July 2024
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For a fixed \(p\geq1\), the main results of the present paper are bounds on the \(L^p\) distance between a pair of densities on Besov spaces over \(\mathbb{R}^d\) or \([0,1]^d\) in terms of powers of the Wasserstein-\(p\) distance between these densities. The powers obtained in these bounds are optimal. These results are illustrated with an example.
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Besov space
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metric inequality
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probability metric
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total variation
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Wasserstein metric
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