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Height and contour processes of Crump-Mode-Jagers forests (II): The Bellman-Harris universality class

Simatos, Florian and Schertzer, Emmanuel Height and contour processes of Crump-Mode-Jagers forests (II): The Bellman-Harris universality class. (2019) Electronic Journal of Probability, 24 (47). 1-38. ISSN 1083-6489

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Official URL: https://doi.org/10.1214/19-EJP307

Abstract

Crump-Mode-Jagers (CMJ) trees generalize Galton-Watson trees by allowing individuals to live for an arbitrary duration and give birth at arbitrary times during their life-time. In this paper, we exhibit a simple condition under which the height and contour processes of CMJ forests belong to the universality class of Bellman-Harris processes. This condition formalizes an asymptotic independence between the chronological and genealogical structures. We show that it is satisfied by a large class of CMJ processes and in particular, quite surprisingly, by CMJ processes with a finite variance offspring distribution. Along the way, we prove a general tightness result.

Item Type:Article
HAL Id:hal-02168469
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Université Pierre et Marie Curie, Paris 6 - UPMC (FRANCE)
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Deposited By: Florian Simatos
Deposited On:28 Jun 2019 12:18

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