IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i2p907-923.html
   My bibliography  Save this article

An entropic interpolation proof of the HWI inequality

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918303454
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2019.04.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2018. "Steering the Distribution of Agents in Mean-Field Games System," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 332-357, October.
    2. 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.
    3. Montacer Essid & Michele Pavon, 2019. "Traversing the Schrödinger Bridge Strait: Robert Fortet’s Marvelous Proof Redux," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 23-60, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:907-923. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.