A strong law of large numbers for branching processes: almost sure spine events

Simon C. Harris; Matthew I. Roberts

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arXiv · 1302.7199

A strong law of large numbers for branching processes: almost sure spine events

Simon C. Harris·Matthew I. Roberts

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Abstract

We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the spine entails the almost sure convergence of a certain sum over particles in the population.

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Simon C. Harris, Matthew I. Roberts. 2013-02-28. A strong law of large numbers for branching processes: almost sure spine events. https://arxiv.org/abs/1302.7199

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