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On the lattice case of an almost-sure renewal theorem for branching random walks

Part of: Markov processes Limit theorems Special processes

Published online by Cambridge University Press:  19 February 2016

Dimitris Gatzouras
Dimitris Gatzouras*
Affiliation:
University of Cambridge
*
∗ Postal address: Department of Mathematics, University of Crete, 714 09 Iraklion, Crete, Greece. Email address: [email protected]
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Abstract

We formulate and verify an almost-sure lattice renewal theorem for branching random walks, whose non-lattice analogue is originally due to Nerman. We also identify the limit in these renewal theorems (both lattice and non-lattice) as the limit of Kingman's well-known martingale multiplied by a deterministic factor.

Keywords

Branching random walkalmost-sure renewal theoremlattice case

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F15: Strong theorems 60K05: Renewal theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 3 , September 2000 , pp. 720 - 737
Copyright
Copyright © Applied Probability Trust 2000 

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References

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