IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v120y2010i5p678-697.html
   My bibliography  Save this article

A limit theorem for trees of alleles in branching processes with rare neutral mutations

Author

Listed:
  • Bertoin, Jean

Abstract

We are interested in the genealogical structure of alleles for a Bienaymé-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial population is large and the mutation rate small. We shall establish that for an appropriate regime, the process of the sizes of the allelic sub-families converges in distribution to a certain continuous state branching process (i.e. a Jirina process) in discrete time. Itô's excursion theory and the Lévy-Itô decomposition of subordinators provide fundamental insights for the results.

Suggested Citation

  • Bertoin, Jean, 2010. "A limit theorem for trees of alleles in branching processes with rare neutral mutations," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 678-697, May.
  • Handle: RePEc:eee:spapps:v:120:y:2010:i:5:p:678-697
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00026-8
    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. Le Gall, Jean-François, 2010. "Itô's excursion theory and random trees," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 721-749, May.
    2. Watanabe, Shinzo, 2010. "Itô's theory of excursion point processes and its developments," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 653-677, May.
    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. Normand, Raoul, 2014. "Two population models with constrained migrations," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1773-1812.
    2. Champagnat, Nicolas & Lambert, Amaury, 2012. "Splitting trees with neutral Poissonian mutations I: Small families," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1003-1033.
    3. Chen, Xinxin, 2013. "Convergence rate of the limit theorem of a Galton–Watson tree with neutral mutations," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 588-595.

    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. Anna Ananova & Rama Cont & Renyuan Xu, 2020. "Model-free Analysis of Dynamic Trading Strategies," Papers 2011.02870, arXiv.org, revised Aug 2023.
    2. Normand, Raoul, 2014. "Two population models with constrained migrations," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1773-1812.
    3. Le Gall, Jean-François, 2010. "Itô's excursion theory and random trees," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 721-749, May.

    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:120:y:2010:i:5:p:678-697. 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.