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Supercritical general branching processes conditioned on extinction are subcritical

2007/12/12 by Peter Jagers, Jagers, Peter, Andreas Nordvall Lagerås +2
Mathematics · Physics and Astronomy · #60J80 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60J80

paper · pdf · doi:10.48550/arxiv.0712.1872

6 pages

arxiv created 2007/12/12 · openalex publication_date 2007/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that a simple, supercritical Bienaymé-Galton-Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where child-bearing may occur at different ages, life span may depend upon reproduction, and the whole course of events is thus affected by conditioning upon extinction.

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