IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i2p503-520.html
   My bibliography  Save this article

Large deviations for empirical measures of mean-field Gibbs measures

Author

Listed:
  • Liu, Wei
  • Wu, Liming

Abstract

In this paper, we show that the empirical measure of mean-field model satisfies the large deviation principle with respect to the weak convergence topology or the stronger Wasserstein metric, under the strong exponential integrability condition on the negative part of the interaction potentials. In contrast to the known results we prove this without any continuity or boundedness condition on the interaction potentials. The proof relies mainly on the law of large numbers and the exponential decoupling inequality of de la Peña for U-statistics.

Suggested Citation

  • Liu, Wei & Wu, Liming, 2020. "Large deviations for empirical measures of mean-field Gibbs measures," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 503-520.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:503-520
    DOI: 10.1016/j.spa.2019.01.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918301145
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2019.01.008?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. Wang, Ran & Wang, Xinyu & Wu, Liming, 2010. "Sanov's theorem in the Wasserstein distance: A necessary and sufficient condition," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 505-512, March.
    Full references (including those not matched with items on IDEAS)

    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. Ran Ji & Miguel A. Lejeune, 2021. "Data-Driven Optimization of Reward-Risk Ratio Measures," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1120-1137, July.
    2. Gao, Fuqing & Wang, Shaochen, 2011. "Asymptotic behavior of the empirical conditional value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 345-352.
    3. Deuschel, Jean-Dominique & Friz, Peter K. & Maurelli, Mario & Slowik, Martin, 2018. "The enhanced Sanov theorem and propagation of chaos," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2228-2269.

    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:503-520. 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.