The Annals of Probability

Supercritical Age Dependent Branching Processes with Generation Dependence

Dean H. Fearn

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Abstract

This paper examines the size, $Z(t)$, of a population as a function of time. $Z(t)$ is just like the ordinary Bellman-Harris age dependent branching process except that the number of daughters born to an individual in the $n$th generation is allowed to depend on $n$. The renewal theory of William Feller and Laplace transform theory are used to obtain the behavior of $EZ(t)$ as $t$ approaches infinity, and the convergence of $Z(t)/E(Z(t))$ in quadratic mean.

Article information

Source
Ann. Probab. Volume 4, Number 1 (1976), 27-37.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996178

Digital Object Identifier
doi:10.1214/aop/1176996178

Mathematical Reviews number (MathSciNet)
MR391287

Zentralblatt MATH identifier
0329.60051

JSTOR
links.jstor.org

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K05: Renewal theory

Keywords
Age dependent branching processes

Citation

Fearn, Dean H. Supercritical Age Dependent Branching Processes with Generation Dependence. Ann. Probab. 4 (1976), no. 1, 27--37. doi:10.1214/aop/1176996178. https://projecteuclid.org/euclid.aop/1176996178


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