Journal of Applied Probability

On a coalescence process and its branching genealogy

Nicolas Grosjean and Thierry Huillet

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Abstract

We define and analyze a coalescent process as a recursive box-filling process whose genealogy is given by an ancestral time-reversed, time-inhomogeneous Bienyamé‒Galton‒Watson process. Special interest is on the expected size of a typical box and its probability of being empty. Special cases leading to exact asymptotic computations are investigated when the coalescing mechanisms are either linear fractional or quadratic.

Article information

Source
J. Appl. Probab. Volume 53, Number 4 (2016), 1156-1165.

Dates
First available in Project Euclid: 7 December 2016

Permanent link to this document
http://projecteuclid.org/euclid.jap/1481132843

Mathematical Reviews number (MathSciNet)
MR3581248

Zentralblatt MATH identifier
06675904

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G20: Generalized stochastic processes

Keywords
Inhomogeneous Bienyamé‒Galton‒Watson process coalescence process genealogy

Citation

Grosjean, Nicolas; Huillet, Thierry. On a coalescence process and its branching genealogy. J. Appl. Probab. 53 (2016), no. 4, 1156--1165. http://projecteuclid.org/euclid.jap/1481132843.


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