Journal of Applied Probability

Coalescence times for the Bienaymé-Galton-Watson process

V. Le

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 51, Number 1 (2014), 209-218.

Dates
First available in Project Euclid: 25 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1395771424

Digital Object Identifier
doi:10.1239/jap/1395771424

Mathematical Reviews number (MathSciNet)
MR3189452

Zentralblatt MATH identifier
1291.60157

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Bienaymé-Galton-Watson process coalescence discrete-state branching process quasistationary distribution

Citation

Le, V. Coalescence times for the Bienaymé-Galton-Watson process. J. Appl. Probab. 51 (2014), no. 1, 209--218. doi:10.1239/jap/1395771424. https://projecteuclid.org/euclid.jap/1395771424


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