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Coalescence Times for the Bienaymé-Galton-Watson Process

Part of: Markov processes

Published online by Cambridge University Press:  30 January 2018

V. Le
V. Le*
Affiliation:
Université de Provence
*
∗ Postal address: Laboratoire d'Analyse Topologie et Probabilités (LATP/UMR 7353), Université d'Aix-Marseille, 39 rue F. Joliot-Curie, F-13453 Marseille cedex 13, France. Email address: levi121286@gmail.com
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Abstract

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We investigate the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a continuous-time Bienaymé-Galton-Watson process founded t units of time ago. We also obtain limiting distributions as t → ∞ in the subcritical case. We extend our results for two individuals to the joint distribution of coalescence times for any finite number of individuals sampled in the current generation.

Keywords

Bienaymé-Galton-Watson processcoalescencediscrete-state branching processquasistationary distribution

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 209 - 218
Copyright
© Applied Probability Trust 

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