Abstract
The HWI inequality is an "interpolation" inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrodinger problem. Our approach consists in making rigorous the Otto-Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.
Lingua originale | English |
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pagine (da-a) | 907-923 |
Numero di pagine | 17 |
Rivista | Stochastic Processes and their Applications |
Volume | 130 |
DOI | |
Stato di pubblicazione | Pubblicato - 2020 |
Keywords
- Entropic interpolations
- Fisher information
- Relative entropy
- Schrodinger problem
- Wasserstein distance