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May 2018 On branching process with rare neutral mutation
Airam Blancas, Víctor Rivero
Bernoulli 24(2): 1576-1612 (May 2018). DOI: 10.3150/16-BEJ907

Abstract

In this paper, we study the genealogical structure of a Galton–Watson process with neutral mutations. Namely, we extend in two directions the asymptotic results obtained in Bertoin [Stochastic Process. Appl. 120 (2010) 678–697]. In the critical case, we construct the version of the model in Bertoin [Stochastic Process. Appl. 120 (2010) 678–697], conditioned not to be extinct. We establish a version of the limit theorems in Bertoin [Stochastic Process. Appl. 120 (2010) 678–697], when the reproduction law has an infinite variance and it is in the domain of attraction of an $\alpha$-stable distribution, both for the unconditioned process and for the process conditioned to nonextinction. In the latter case, we obtain the convergence (after re-normalization) of the allelic sub-populations towards a tree indexed CSBP with immigration.

Citation

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Airam Blancas. Víctor Rivero. "On branching process with rare neutral mutation." Bernoulli 24 (2) 1576 - 1612, May 2018. https://doi.org/10.3150/16-BEJ907

Information

Received: 1 August 2015; Revised: 1 June 2016; Published: May 2018
First available in Project Euclid: 21 September 2017

zbMATH: 06778373
MathSciNet: MR3706802
Digital Object Identifier: 10.3150/16-BEJ907

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 2 • May 2018
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