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


  • Chen, Xinxin


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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:588-595
    DOI: 10.1016/j.spl.2012.10.029

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    References listed on IDEAS

    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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