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Convergence rate of the limit theorem of a Galton–Watson tree with neutral mutations

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  • Chen, Xinxin
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    Abstract

    We consider a Galton–Watson branching process with neutral mutations (infinite alleles model), and we decompose the entire population into sub-families of individuals carrying the same allele. Bertoin (2010) describes the asymptotic shape of the process of the sizes of the allelic sub-families when the initial population is large and the mutation rate small. The limit in law is a certain continuous state-space branching process (CSBP). In the present work, we obtain a Central Limit Theorem, thus completing Bertoin’s work.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212004014
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 2 ()
    Pages: 588-595

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:588-595

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    Related research

    Keywords: Branching process; Lévy-Itô decomposition; Donsker’s invariance principle; Skorohod’s representation;

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    1. 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.
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