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On a coalescence process and its branching genealogy

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  09 December 2016

Nicolas Grosjean  and
Thierry Huillet
Nicolas Grosjean*
Affiliation:
Université de Cergy-Pontoise
Thierry Huillet*
Affiliation:
Université de Cergy-Pontoise
*
* Postal address: Laboratoire de Physique Théorique et Modélisation, CNRS-UMR 8089, Université de Cergy-Pontoise, 2 Avenue Adolphe Chauvin, Cergy-Pontoise, 95302, France.
* Postal address: Laboratoire de Physique Théorique et Modélisation, CNRS-UMR 8089, Université de Cergy-Pontoise, 2 Avenue Adolphe Chauvin, Cergy-Pontoise, 95302, France.
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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.

Keywords

Inhomogeneous Bienyamé‒Galton‒Watson processcoalescence processgenealogy

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G20: Generalized stochastic processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 1156 - 1165
Copyright
Copyright © Applied Probability Trust 2016 

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