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An Almost-Sure Renewal Theorem for Branching Random Walks on the Line

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Matthias Meiners
Matthias Meiners*
Affiliation:
Uppsala University
*
∗Postal address: Department of Mathematics, Uppsala University, 75106 Uppsala, Sweden. Email address: matthias.meiners@math.uu.se
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Abstract

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In the present paper an almost-sure renewal theorem for branching random walks (BRWs) on the real line is formulated and established. The theorem constitutes a generalization of Nerman's theorem on the almost-sure convergence of Malthus normed supercritical Crump-Mode-Jagers branching processes counted with general characteristic and Gatouras' almost-sure renewal theorem for BRWs on a lattice.

Keywords

Branching random walkmartingalerenewal theorem

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K05: Renewal theory
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 3 , September 2010 , pp. 811 - 825
Copyright
Copyright © Applied Probability Trust 2010 

Footnotes

Research supported by DFG grant Me 3625/1-1.

References

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