IDEAS home Printed from https://ideas.repec.org/p/hub/wpecon/200717.html
   My bibliography  Save this paper

Singles in a Markov chain

Author

Listed:
  • Omey, Edward

    () (Hogeschool-Universiteit Brussel (HUB), Belgium)

  • Van Gulck, Stefan

    () (Hogeschool-Universiteit Brussel (HUB), Belgium)

Abstract

Let fXi; i _ 1g denote a sequence of variables that take values in f0; 1g and suppose that the sequence forms a Markov chain with transition matrix P and with initial distribution (q; p) = (P(X1 = 0); P(X1 = 1)). Several authors have studied the quantities Sn, Y (r) and AR(n), where Sn = Pn i=1 Xi denotes the number of successes, where Y (r) denotes the number of experiments up to the r??th success and where AR(n) denotes the number of runs. In the present paper we study the number of singles AS(n) in the vector (X1;X2; :::;Xn). A single in a sequence is an isolated value of 0 or 1, i.e. a run of lenght 1. Among others we prove a central limit theorem for AS(n).

Suggested Citation

  • Omey, Edward & Van Gulck, Stefan, 2007. "Singles in a Markov chain," Working Papers 2007/17, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
  • Handle: RePEc:hub:wpecon:200717
    as

    Download full text from publisher

    File URL: http://lirias.hubrussel.be/handle/123456789/2187
    Download Restriction: no

    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:hub:wpecon:200717. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sabine Janssens). General contact details of provider: http://edirc.repec.org/data/emhubbe.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.