## The Annals of Probability

### 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

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