On a $T_1$ Transport inequality for the adapted Wasserstein distance
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909961623175168 |
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| author | Park, Jonghwa |
| author_facet | Park, Jonghwa |
| contents | The $L^1$ transport-entropy inequality (or $T_1$ inequality), which bounds the $1$-Wasserstein distance in terms of the relative entropy, is known to characterize Gaussian concentration. To extend the $T_1$ inequality to laws of discrete-time processes while preserving their temporal structure, we investigate the adapted $T_1$ inequality which relates the $1$-adapted Wasserstein distance to the relative entropy. Building on the Bolley--Villani inequality, we establish the adapted $T_1$ inequality under the same moment assumption as the classical $T_1$ inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a $T_1$ Transport inequality for the adapted Wasserstein distance Park, Jonghwa Probability Statistics Theory 60E15, 60G07 (Primary) 60B10, 62B10 (Secondary) The $L^1$ transport-entropy inequality (or $T_1$ inequality), which bounds the $1$-Wasserstein distance in terms of the relative entropy, is known to characterize Gaussian concentration. To extend the $T_1$ inequality to laws of discrete-time processes while preserving their temporal structure, we investigate the adapted $T_1$ inequality which relates the $1$-adapted Wasserstein distance to the relative entropy. Building on the Bolley--Villani inequality, we establish the adapted $T_1$ inequality under the same moment assumption as the classical $T_1$ inequality. |
| title | On a $T_1$ Transport inequality for the adapted Wasserstein distance |
| topic | Probability Statistics Theory 60E15, 60G07 (Primary) 60B10, 62B10 (Secondary) |
| url | https://arxiv.org/abs/2507.19215 |