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The growth of general population-size-dependent branching processes year by year

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Peter Jagers  and
Serik Sagitov
Peter Jagers*
Affiliation:
Chalmers University/University of Göteborg
Serik Sagitov*
Affiliation:
Chalmers University/University of Göteborg
*
∗Postal address: School of Mathematical and Computing Sciences, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden
∗Postal address: School of Mathematical and Computing Sciences, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden
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Abstract

We study discrete-time population models where the nearest future of an individual may depend on the individual's life-stage (age and reproduction history) and the current population size. A criterion is given for whether there is a positive probability that the population survives forever. We identify the cases when population size grows exponentially and linearly and show that in the latter population size scaled by time is asymptotically Γ-distributed.

Keywords

Population-size dependencebranching processmultitype Galton-Watson processstochastic difference equationdemographic models

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F25: $L^p$-limit theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000 , pp. 1 - 14
Copyright
Copyright © 2000 by The Applied Probability Trust 

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Footnotes

This work is part of the Bank of Sweden Tercentenary Foundation project Dependence and Interaction in Stochastic Population Dynamics

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