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November 1999 Branching processes with dependence but homogeneous growth
Peter Jagers
Ann. Appl. Probab. 9(4): 1160-1174 (November 1999). DOI: 10.1214/aoap/1029962868


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.


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Peter Jagers. "Branching processes with dependence but homogeneous growth." Ann. Appl. Probab. 9 (4) 1160 - 1174, November 1999.


Published: November 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0960.60066
MathSciNet: MR1728558
Digital Object Identifier: 10.1214/aoap/1029962868

Primary: 60J80
Secondary: 60F25 , 92A15

Keywords: branching processes , cell kinetics , Population dynamics , population size dependence

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.9 • No. 4 • November 1999
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