Coupling and population dependence in branching processes
type: Item
instance of: scholarly article
title: Coupling and population dependence in branching processes
zbMATH Open document ID: 0884.60084
author: P. Jagers
published in: The Annals of Applied Probability
publication date: 1998-03-19T00:00:00Z
review text: There are considered general, abstract multitype supercritical branching processes, where individual reproduction may be affected by properties of the whole population, such as its size or history. There is focused the situation upon that where reproduction tends to decrease as population grows, the limiting individual reproductions being those of a traditional (population independent) supercritical branching process. There are found conditions for the population dependence not to matter so that asymptotically, classical Malthusian growth shows up with the same parameters as those of limiting population where individuals reproduce independently, once they have been born into the population and obtained their types. For investigations there are defined imaginary types of particles. The idea is to couple actual and imaginary reproductions of individuals and to extend the methods of \textit{P. Jagers} in his papers [Stochastic Processes Appl. 32, No. 2, 183-212 (1989; Zbl 0678.92009)] and [Classical and modern branching processes. IMA Vol. Math. Appl. 84, 127-139 (1997; Zbl 0867.60062)]. There are made some applications to a tumor model with quiescence.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60F25
zbMATH DE Number: 1051763
zbMATH Keywords: general branching processes
zbMATH Keywords: population dynamics
zbMATH Keywords: cell kinetics
zbMATH Keywords: population size dependence
zbMATH Keywords: supercritical
reviewed by: Valentin Topchii
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1034625331
OpenAlex ID: W2074832826
DOI: 10.1214/AOAP/1034625331
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description: scientific article; zbMATH DE number 1051763