IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v122y2012i11p3740-3756.html
   My bibliography  Save this article

Total variation approximation for quasi-equilibrium distributions, II

Author

Listed:
  • Barbour, A.D.
  • Pollett, P.K.

Abstract

Quasi-stationary distributions have been used in biology to describe the steady state behaviour of Markovian population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. However, they have substantial drawbacks; a Markov process may not possess any, or may have several, and their probabilities can be very difficult to determine. Here, we consider conditions under which an apparent stochastic equilibrium distribution can be identified and computed, irrespective of whether a quasi-stationary distribution exists, or is unique; we call it a quasi-equilibrium distribution. The results are applied to multi-dimensional Markov population processes.

Suggested Citation

  • Barbour, A.D. & Pollett, P.K., 2012. "Total variation approximation for quasi-equilibrium distributions, II," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3740-3756.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:11:p:3740-3756
    DOI: 10.1016/j.spa.2012.07.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441491200155X
    Download Restriction: Full text for ScienceDirect subscribers only

    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:spapps:v:122:y:2012:i:11:p:3740-3756. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.