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

Xinxin Chen

Statistics & Probability Letters, 2013, vol. 83, issue 2, 588-595

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.

Keywords: Branching process; Lévy-Itô decomposition; Donsker’s invariance principle; Skorohod’s representation (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2012.10.029

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