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An entropic interpolation proof of the HWI inequality

Author

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  • Gentil, Ivan
  • Léonard, Christian
  • Ripani, Luigia
  • Tamanini, Luca

Abstract

The HWI inequality is an “interpolation”inequality between the EntropyH, the Fisher informationI and the Wasserstein distanceW. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrödinger 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.

Suggested Citation

  • Gentil, Ivan & Léonard, Christian & Ripani, Luigia & Tamanini, Luca, 2020. "An entropic interpolation proof of the HWI inequality," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 907-923.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:907-923
    DOI: 10.1016/j.spa.2019.04.002
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    References listed on IDEAS

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    1. Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2016. "On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 671-691, May.
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    Cited by:

    1. Conforti, Giovanni & Léonard, Christian, 2022. "Time reversal of Markov processes with jumps under a finite entropy condition," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 85-124.

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