IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v20y2007i3d10.1007_s10959-007-0065-2.html
   My bibliography  Save this article

A Characteristic Martingale Related to the Counting Process of Records

Author

Listed:
  • Raúl Gouet

    (Universidad de Chile)

  • F. Javier López

    (Universidad de Zaragoza)

  • Gerardo Sanz

    (Universidad de Zaragoza)

Abstract

Let (X n ) be a sequence of nonnegative, integrable, independent and identically distributed random variables, with common distribution function F. We consider the problem of finding all distribution functions F such that N n −cM n is a discrete time martingale, where N n is the counting process of upper records, M n =max {X 1,…,X n } is the process of partial maxima and c is a positive constant. We solve the problem by explicitly giving the solution with finite support and using this for constructing the solution for the general case by a limiting process. We show that the set of solutions can be parameterized by their support and the mass at the leftmost point of the support.

Suggested Citation

  • Raúl Gouet & F. Javier López & Gerardo Sanz, 2007. "A Characteristic Martingale Related to the Counting Process of Records," Journal of Theoretical Probability, Springer, vol. 20(3), pages 443-455, September.
    • Handle: RePEc:spr:jotpro:v:20:y:2007:i:3:d:10.1007_s10959-007-0065-2
    DOI: 10.1007/s10959-007-0065-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-007-0065-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-007-0065-2?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:spr:jotpro:v:20:y:2007:i:3:d:10.1007_s10959-007-0065-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.