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February, 1976 Convergence of the Age Distribution in the One-Dimensional Supercritical Age-Dependent Branching Process
K. B. Athreya, N. Kaplan
Ann. Probab. 4(1): 38-50 (February, 1976). DOI: 10.1214/aop/1176996179

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.

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K. B. Athreya. N. Kaplan. "Convergence of the Age Distribution in the One-Dimensional Supercritical Age-Dependent Branching Process." Ann. Probab. 4 (1) 38 - 50, February, 1976. https://doi.org/10.1214/aop/1176996179

Information

Published: February, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0356.60048
MathSciNet: MR400431
Digital Object Identifier: 10.1214/aop/1176996179

Subjects:
Primary: 60J80
Secondary: 60J85

Keywords: age-dependent branching process , age-distribution , convergence , supercritical

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 1 • February, 1976
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