Open Access
November 2008 General branching processes in discrete time as random trees
Peter Jagers, Serik Sagitov
Bernoulli 14(4): 949-962 (November 2008). DOI: 10.3150/08-BEJ138

Abstract

The simple Galton–Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random trees, each vertex being an individual of the family tree. This viewpoint has led to new insights and a revival of classical theory.

We show how a similar reinterpretation can shed new light on the more interesting forms of branching processes that allow repeated bearings and, thus, overlapping generations. In particular, we use the stable pedigree law to give a transparent description of a size-biased version of general branching processes in discrete time. This allows us to analyze the $x \log x$ condition for exponential growth of supercritical general processes as well as relation between simple Galton–Watson and more general branching processes.

Citation

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Peter Jagers. Serik Sagitov. "General branching processes in discrete time as random trees." Bernoulli 14 (4) 949 - 962, November 2008. https://doi.org/10.3150/08-BEJ138

Information

Published: November 2008
First available in Project Euclid: 6 November 2008

zbMATH: 1157.60338
MathSciNet: MR2543581
Digital Object Identifier: 10.3150/08-BEJ138

Keywords: Crump–Mode–Jagers , Galton–Watson , Random trees , size-biased distributions

Rights: Copyright © 2008 Bernoulli Society for Mathematical Statistics and Probability

Vol.14 • No. 4 • November 2008
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