The Annals of Probability

Convergence of the Age Distribution in the One-Dimensional Supercritical Age-Dependent Branching Process

K. B. Athreya and N. Kaplan

Full-text: Open access

Abstract

The age distribution for a supercritical Bellman-Harris process is proven to converge in probability to a deterministic distribution under assumptions slightly more than finite first moment. If the usual "$j \log j$" condition holds, then the convergence can be strengthened to hold w.p. 1. As a corollary to this result, the population size, properly normalized is shown to converge w.p. 1 to a nondegenerate random variable under the "$j \log j$" assumption.

Article information

Source
Ann. Probab. Volume 4, Number 1 (1976), 38-50.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996179

Digital Object Identifier
doi:10.1214/aop/1176996179

Mathematical Reviews number (MathSciNet)
MR400431

Zentralblatt MATH identifier
0356.60048

JSTOR
links.jstor.org

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes [See also 92Dxx]

Keywords
Age-dependent branching process age-distribution supercritical convergence

Citation

Athreya, K. B.; Kaplan, N. Convergence of the Age Distribution in the One-Dimensional Supercritical Age-Dependent Branching Process. Ann. Probab. 4 (1976), no. 1, 38--50. doi:10.1214/aop/1176996179. https://projecteuclid.org/euclid.aop/1176996179


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