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

2013/02/28 by Simon C. Harris, Harris, Simon C., Matthew I. Roberts +1
Mathematics · Physics and Astronomy · #60J80 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1302.7199

openalex publication_date 2013/02/28 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

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

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