The Annals of Applied Probability

Branching processes with dependence but homogeneous growth

Peter Jagers

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Abstract

A (general) branching process, where individuals need not reproduce independently, satisfies a homogeneous growth condition if, vaguely, one would not expect the progeny from any one individual to make out more than its proper fraction of the whole population at any time in the future. This notion is made precise, and it is shown how it entails classical Malthusian growth in supercritical cases, in particular for population size-dependent Bienaymé-Galton-Watson and Markov branching processes, and for nondecreasing age-dependent processes with continuous life span distributions.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 4 (1999), 1160-1174.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962868

Digital Object Identifier
doi:10.1214/aoap/1029962868

Mathematical Reviews number (MathSciNet)
MR1728558

Zentralblatt MATH identifier
0960.60066

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F25: $L^p$-limit theorems 92A15

Keywords
Branching processes population dynamics cell kinetics population size dependence

Citation

Jagers, Peter. Branching processes with dependence but homogeneous growth. Ann. Appl. Probab. 9 (1999), no. 4, 1160--1174. doi:10.1214/aoap/1029962868. https://projecteuclid.org/euclid.aoap/1029962868


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