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November 2004 Asymptotic genealogy of a critical branching process
Lea Popovic
Ann. Appl. Probab. 14(4): 2120-2148 (November 2004). DOI: 10.1214/105051604000000486

Abstract

Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the smallest subtree containing the genealogy of the extant individuals together with the genealogy of the recorded extinct individuals. We introduce a novel representation of such subtrees in terms of a point-process, and provide asymptotic results on the distribution of this point-process as the number of extant individuals increases. We motivate the study within the scope of a coherent analysis for an a priori model for macroevolution.

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Lea Popovic. "Asymptotic genealogy of a critical branching process." Ann. Appl. Probab. 14 (4) 2120 - 2148, November 2004. https://doi.org/10.1214/105051604000000486

Information

Published: November 2004
First available in Project Euclid: 5 November 2004

zbMATH: 1062.92048
MathSciNet: MR2100386
Digital Object Identifier: 10.1214/105051604000000486

Subjects:
Primary: 60J85
Secondary: 60J65 , 92D15

Keywords: Brownian excursion , Critical branching process , Galton–Watson process , genealogy , point process , Random tree

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 4 • November 2004
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