IDEAS home Printed from https://ideas.repec.org/p/pav/wpaper/112.html
   My bibliography  Save this paper

A Central Limit Theorem and Its Applications to Multicolor Randomly Reinforced Urns

Author

Listed:
  • Patrizia Berti

    (Department of Mathematics, University of Modena and Reggio Emilia)

  • Irene Crimaldi

    (Università di Bologna)

  • Luca Pratelli

    (Accademia Navale di Livorno)

  • Pietro Rigo

    (Department of Economics and Quantitative Methods, University of Pavia)

Abstract

Let (Xn) be a sequence of integrable real random variables, adapted to a filtration (Gn). Define: Cn = n^(1/2) {1/n SUM(k=1:n) Xk - E(Xn+1 | Gn) } and Dn = n^(1/2){ E(Xn+1 | Gn)-Z } where Z is the a.s. limit of E(Xn+1 | Gn) (assumed to exist). Conditions for (Cn,Dn) --> N(0,U) × N(0,V) stably are given, where U, V are certain random variables. In particular, under such conditions, one obtains n^(1/2) { 1/n SUM(k=1:n) Xk - Z } = Cn + Dn --> N(0,U+V) stably. This CLT has natural applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced generalized Polya urns.

Suggested Citation

  • Patrizia Berti & Irene Crimaldi & Luca Pratelli & Pietro Rigo, 2010. "A Central Limit Theorem and Its Applications to Multicolor Randomly Reinforced Urns," Quaderni di Dipartimento 112, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:112
    as

    Download full text from publisher

    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/wpaper/q112.pdf
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2010. "Limit Theorems for Empirical Processes Based on Dependent Data," Quaderni di Dipartimento 132, University of Pavia, Department of Economics and Quantitative Methods.
    2. Crimaldi, Irene & Louis, Pierre-Yves & Minelli, Ida G., 2022. "An urn model with random multiple drawing and random addition," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 270-299.

    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:pav:wpaper:112. 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: Paolo Bonomolo (email available below). General contact details of provider: https://edirc.repec.org/data/dppavit.html .

    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.