IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v57y1995i1p1-10.html
   My bibliography  Save this article

Compactness in the theory of large deviations

Author

Listed:
  • O'Brien, George L.
  • Vervaat, Wim

Abstract

Large-deviation principles (LDPs) are expressed as the vague or narrow convergence of sequences of set functions called capacities. Compactness and other topological properties of the collection of capacities are then used in conjunction with Varadhan's integral theorem to reduce the proof of LDPs to the problem of showing that a certain system of equations has a unique solution. As applications of these ideas, we present short proofs of extended versions of a theorem of Bryc and of the Gärtner-Ellis theorem.

Suggested Citation

  • O'Brien, George L. & Vervaat, Wim, 1995. "Compactness in the theory of large deviations," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 1-10, May.
    • Handle: RePEc:eee:spapps:v:57:y:1995:i:1:p:1-10
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(95)00007-T
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Ganguly, Arnab, 2018. "Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2179-2227.
    2. Nyrhinen, Harri, 2007. "Convex large deviation rate functions under mixtures of linear transformations, with an application to ruin theory," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 947-959, July.

    More about this item

    Statistics

    Access and download statistics

    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:57:y:1995:i:1:p:1-10. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.