IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v201y2023ics0167715223001050.html
   My bibliography  Save this article

A Galton–Watson process with a threshold at 1 and an immigration at 0

Author

Listed:
  • Lu, Dawei
  • Lv, Huangding

Abstract

In this paper we consider a special class of population-size-dependent branching processes, which can also be seen as an extension of Galton–Watson processes with state-dependent immigration (GWPSDI). The model is formulated as follows. Let Zn be the size of individuals belonging to the nth generation of a population. If Zn>1, the population evolves as a critical Galton–Watson process with finite variance; if Zn=1, the population evolves as another Galton–Watson process; if Zn=0, Zn+1 is drawn from a fixed immigration distribution. Based on the technical routes in Foster (1971) and Pakes (1971), some asymptotic results identical with those of GWPSDI are obtained by detailed computations.

Suggested Citation

  • Lu, Dawei & Lv, Huangding, 2023. "A Galton–Watson process with a threshold at 1 and an immigration at 0," Statistics & Probability Letters, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:stapro:v:201:y:2023:i:c:s0167715223001050
    DOI: 10.1016/j.spl.2023.109881
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715223001050
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2023.109881?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:eee:stapro:v:201:y:2023:i:c:s0167715223001050. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/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.