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On the limit of a supercritical branching process

Published online by Cambridge University Press:  14 July 2016

N. H. Bingham
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Abstract

Let W be the usual almost-sure limit random variable in a supercritical simple branching process; we study its tail behaviour. For the left tail, we distinguish two cases, the ‘Schröder' and ‘Böttcher' cases; both appear in work of Harris and Dubuc. The Schröder case is related to work of Karlin and McGregor on embeddability in continuous-time (Markov) branching processes. New results are obtained for the Böttcher case; there are links with recent work of Barlow and Perkins on Brownian motion on a fractal. The right tail is also considered. Use is made of recent progress in Tauberian theory.

Keywords

FUNCTIONAL EQUATIONSITERATIONTAUBERIAN THEORYEMBEDDABILITYBROWNIAN MOTIONFRACTALINFINITE DIVISIBILITY
Type
Part 6 - The Analysis of Stochastic Phenomena
Information
Journal of Applied Probability , Volume 25 , Issue A , 1988 , pp. 215 - 228
Copyright
Copyright © Applied Probability Trust 1988 

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