The Annals of Probability

An Age-Dependent Model with Parental Survival

Thomas H. Savits

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Abstract

We consider an age-dependent model which not only allows the generating function to be age-dependent, but also allows the parent to reproduce several times during its lifetime. By using the notion of $\vee$-space-time harmonic functions, we study the behavior of $Z_t$, the number of particles alive at time $t$, in the supercritical case. In particular we obtain results which are analogous to the classically known results for the Bellman-Harris model; in fact, we obtain convergence in probability.

Article information

Source
Ann. Probab., Volume 4, Number 3 (1976), 382-392.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996087

Digital Object Identifier
doi:10.1214/aop/1176996087

Mathematical Reviews number (MathSciNet)
MR402961

Zentralblatt MATH identifier
0356.60049

JSTOR
links.jstor.org

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

Keywords
Age-dependent process parental survival harmonic function space-time martingale convergence in law

Citation

Savits, Thomas H. An Age-Dependent Model with Parental Survival. Ann. Probab. 4 (1976), no. 3, 382--392. doi:10.1214/aop/1176996087. https://projecteuclid.org/euclid.aop/1176996087


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