The Annals of Probability
- Ann. Probab.
- Volume 4, Number 1 (1976), 38-50.
Convergence of the Age Distribution in the One-Dimensional Supercritical Age-Dependent Branching Process
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
