IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v50y1994i1p57-71.html
   My bibliography  Save this article

Large deviations for renewal processes

Author

Listed:
  • Tiefeng, Jiang

Abstract

Let {Xn, n [greater-or-equal, slanted]1} be a sequence of identically distributed real random variables with EX1 = [mu] > 0. Define Sn=[Sigma]ni=1Xi and N[alpha](t) = inf{n[greater-or-equal, slanted]1;Sn>n[alpha]t}, where t>0, [alpha][set membership, variant][0, 1) and the infimum o f the empty set is defined to be +[infinity]. Let P[alpha],t be the distribution of N[alpha](t)/t1/(1-[alpha]), t> 0. In this paper, we establish the large deviation principle for {P[alpha], t; t> 0} when {Xn; n[greater-or-equal, slanted] 1 } is a sequence of i.i.d. random variables or, more generally, an exchangeable sequence.

Suggested Citation

  • Tiefeng, Jiang, 1994. "Large deviations for renewal processes," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 57-71, March.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:1:p:57-71
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(94)90147-3
    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. Jeffrey Collamore & Andrea Höing, 2007. "Small-time ruin for a financial process modulated by a Harris recurrent Markov chain," Finance and Stochastics, Springer, vol. 11(3), pages 299-322, July.
    2. Cattiaux, Patrick & Colombani, Laetitia & Costa, Manon, 2023. "Asymptotic deviation bounds for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 85-105.

    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:50:y:1994:i:1:p:57-71. 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.