IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v88y2000i2p177-193.html
   My bibliography  Save this article

Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Author

Listed:
  • Chen, Anyue
  • Renshaw, Eric

Abstract

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate [alpha]j. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.

Suggested Citation

  • Chen, Anyue & Renshaw, Eric, 2000. "Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 177-193, August.
    • Handle: RePEc:eee:spapps:v:88:y:2000:i:2:p:177-193
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(99)00125-8
    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.

    References listed on IDEAS

    as
    1. Chen, Anyue & Renshaw, Eric, 1995. "Markov branching processes regulated by emigration and large immigration," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 339-359, June.
    2. Chen, Anyue & Renshaw, Eric, 1993. "Recurrence of Markov branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 231-242, April.
    3. Pakes, Anthony G., 1993. "Absorbing Markov and branching processes with instantaneous resurrection," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 85-106, October.
    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. Anyue Chen, 2020. "Resolvent Decomposition Theorems and Their Application in Denumerable Markov Processes with Instantaneous States," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2089-2118, December.
    2. Renshaw, Eric, 2004. "Metropolis-Hastings from a stochastic population dynamics perspective," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 765-786, May.

    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. Anyue Chen, 2020. "Resolvent Decomposition Theorems and Their Application in Denumerable Markov Processes with Instantaneous States," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2089-2118, December.
    2. Khrystyna Prysyazhnyk & Iryna Bazylevych & Ludmila Mitkova & Iryna Ivanochko, 2021. "Period-Life of a Branching Process with Migration and Continuous Time," Mathematics, MDPI, vol. 9(8), pages 1-10, April.
    3. Chen, Anyue & Renshaw, Eric, 1995. "Markov branching processes regulated by emigration and large immigration," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 339-359, June.
    4. Renshaw, Eric, 2004. "Metropolis-Hastings from a stochastic population dynamics perspective," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 765-786, May.
    5. Wang, Juan & Li, Junping, 2013. "Uniqueness, recurrence and decay properties of collision branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1603-1612.

    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:88:y:2000:i:2:p:177-193. 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.