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On the lattice case of an almost-sure renewal theorem for branching random walks
Part of
Dimitris Gatzouras
Journal:

Advances in Applied Probability / Volume 32 / Issue 3 / September 2000

Published online by Cambridge University Press:

19 February 2016, pp. 720-737

Print publication:

September 2000
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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.

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