Article ID Journal Published Year Pages File Type
1153181 Statistics & Probability Letters 2013 8 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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