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June, 1981 Necessary and Sufficient Lifetime Conditions for Normed Convergence of Critical Age-Dependent Processes with Infinite Variance
Martin I. Goldstein, Fred M. Hoppe
Ann. Probab. 9(3): 490-497 (June, 1981). DOI: 10.1214/aop/1176994421

Abstract

The critical age-dependent branching process with offspring p.g.f. of the form $f(s) = s + (1 - s)^{1 + \alpha}L(1 - s), 0 < \alpha \leq 1, L$ slowly varying at 0, is investigated. We generalize Kesten's unpublished necessary condition to establish N.A.S.C. on the tail of the lifetime distribution for existence of a nondegenerate normalized conditioned limit law and pose several related questions.

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Martin I. Goldstein. Fred M. Hoppe. "Necessary and Sufficient Lifetime Conditions for Normed Convergence of Critical Age-Dependent Processes with Infinite Variance." Ann. Probab. 9 (3) 490 - 497, June, 1981. https://doi.org/10.1214/aop/1176994421

Information

Published: June, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0461.60093
MathSciNet: MR614633
Digital Object Identifier: 10.1214/aop/1176994421

Subjects:
Primary: 60K99
Secondary: 60J80

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 3 • June, 1981
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