IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v7y2005i4d10.1007_s11009-005-5005-y.html
   My bibliography  Save this article

Uniqueness and Extinction of Weighted Markov Branching Processes

Author

Listed:
  • Anyue Chen

    (The University of Greenwich
    University of Hong Kong)

  • Junping Li

    (The University of Greenwich
    Central South University)

  • N. I. Ramesh

    (The University of Greenwich)

Abstract

This paper focuses on discussing some basic properties of the weighted Markov branching process which is a natural generalisation of the ordinary Markov branching process. The regularity and uniqueness criteria, which are very easy to verify, are firstly established. Some important characteristics regarding the hitting times of such structure are obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and then the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained.

Suggested Citation

  • Anyue Chen & Junping Li & N. I. Ramesh, 2005. "Uniqueness and Extinction of Weighted Markov Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 489-516, December.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:4:d:10.1007_s11009-005-5005-y
    DOI: 10.1007/s11009-005-5005-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-005-5005-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/s11009-005-5005-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. Chen, Anyue & Li, Junping & Ramesh, N.I., 2008. "Probabilistic approach in weighted Markov branching processes," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 771-779, April.
    2. Anyue Chen & Phil Pollett & Junping Li & Hanjun Zhang, 2010. "Uniqueness, Extinction and Explosivity of Generalised Markov Branching Processes with Pairwise Interaction," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 511-531, September.
    3. Li Junping & Chen Anyue, 2013. "The Decay Parameter and Invariant Measures for Markovian Bulk-Arrival Queues with Control at Idle Time," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 467-484, June.

    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:7:y:2005:i:4:d:10.1007_s11009-005-5005-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.