IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v122y2012i6p2400-2410.html
   My bibliography  Save this article

Conditions for the existence of quasi-stationary distributions for birth–death processes with killing

Author

Listed:
  • van Doorn, Erik A.

Abstract

We consider birth–death processes on the nonnegative integers, where {1,2,…} is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 (killing) may occur from any state. Assuming that absorption at 0 is certain we are interested in additional conditions on the transition rates for the existence of a quasi-stationary distribution. Inspired by results of Kolb and Steinsaltz [M. Kolb, D. Steinsaltz, Quasilimiting behavior for one-dimensional diffusions with killing, Ann. Probab. 40 (2012) 162–212] we show that a quasi-stationary distribution exists if the decay rate of the process is positive and exceeds at most finitely many killing rates. If the decay rate is positive and smaller than at most finitely many killing rates then a quasi-stationary distribution exists if and only if the process one obtains by setting all killing rates equal to zero is recurrent.

Suggested Citation

  • van Doorn, Erik A., 2012. "Conditions for the existence of quasi-stationary distributions for birth–death processes with killing," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2400-2410.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:6:p:2400-2410
    DOI: 10.1016/j.spa.2012.03.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912000555
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2012.03.014?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.

    References listed on IDEAS

    as
    1. van Doorn, Erik A. & Zeifman, Alexander I., 2005. "Birth-death processes with killing," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 33-42, April.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peter Keller & Sylvie Rœlly & Angelo Valleriani, 2015. "A Quasi Random Walk to Model a Biological Transport Process," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 125-137, March.

    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:6:p:2400-2410. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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/505572/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.