IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v8y2006i4d10.1007_s11009-006-0424-y.html
   My bibliography  Save this article

Quasi-stationary Distributions for a Class of Discrete-time Markov Chains

Author

Listed:
  • Pauline Coolen-Schrijner

    (Durham University)

  • Erik A. Doorn

    (University of Twente)

Abstract

This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution—actually an infinite family of quasi-stationary distributions— if and only if absorption is certain and the chain is geometrically transient. If we widen the setting by allowing absorption in one step (killing) from any state, the two conditions are still necessary, but no longer sufficient. We show that the birth–death-type of behaviour prevails as long as the number of states in which killing can occur is finite. But if there are infinitely many such states, and if the chain is geometrically transient and absorption certain, then there may be 0, 1, or infinitely many quasi-stationary distributions. Examples of each type of behaviour are presented. We also survey and supplement the theory of quasi-stationary distributions for discrete-time Markov chains in general.

Suggested Citation

  • Pauline Coolen-Schrijner & Erik A. Doorn, 2006. "Quasi-stationary Distributions for a Class of Discrete-time Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 449-465, December.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:4:d:10.1007_s11009-006-0424-y
    DOI: 10.1007/s11009-006-0424-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-006-0424-y
    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/s11009-006-0424-y?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.

    Citations

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


    Cited by:

    1. Artalejo, J.R., 2012. "On the time to extinction from quasi-stationarity: A unified approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4483-4486.

    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:metcap:v:8:y:2006:i:4:d:10.1007_s11009-006-0424-y. 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.