IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v87y2014icp105-107.html
   My bibliography  Save this article

On convergence of randomly indexed sequences; a counterexample based on the St. Petersburg game

Author

Listed:
  • Gut, Allan

Abstract

If Y1,Y2,… is a sequence of random variables such that Yn⟶a.s.Y as n→∞, and {τ(t),t≥0} is a family of “indices” such that τ(t)⟶a.s.∞ as t→∞, then it is pretty obvious that Yτ(t)⟶a.s.Y as t→∞. However, if one relaxes one of ⟶a.s. to ⟶p and lets the other one remain as is, then one of the resulting conclusions holds, whereas the other one does not. In this note we provide a “more natural” counterexample than the original one due to Richter (1965), followed by a minor extension.

Suggested Citation

  • Gut, Allan, 2014. "On convergence of randomly indexed sequences; a counterexample based on the St. Petersburg game," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 105-107.
    • Handle: RePEc:eee:stapro:v:87:y:2014:i:c:p:105-107
    DOI: 10.1016/j.spl.2014.01.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214000224
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.01.011?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.

    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:stapro:v:87:y:2014:i:c:p:105-107. 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/622892/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.