Journal of Applied Probability

On a coalescence process and its branching genealogy

Nicolas Grosjean and Thierry Huillet

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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

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

First available in Project Euclid: 7 December 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Inhomogeneous Bienyamé‒Galton‒Watson process coalescence process genealogy


Grosjean, Nicolas; Huillet, Thierry. On a coalescence process and its branching genealogy. J. Appl. Probab. 53 (2016), no. 4, 1156--1165.

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