On a $T_1$ Transport inequality for the adapted Wasserstein distance

Jonghwa Park

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arXiv · 2507.19215

On a $T_1$ Transport inequality for the adapted Wasserstein distance

Jonghwa Park

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Abstract

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.

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Jonghwa Park. 2025-07-25. On a $T_1$ Transport inequality for the adapted Wasserstein distance. https://arxiv.org/abs/2507.19215

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