On Supercritical Branching Processes with Emigration

2020/08/12 by Georg Braun, Braun, Georg
Mathematics · Medicine · Physics and Astronomy · #60J10 #60J80 #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60J10 #msc:60J80

paper · pdf · doi:10.48550/arxiv.2008.05178

23 pages

arxiv created 2020/08/12 · openalex publication_date 2020/08/12 · arxiv updated 2020/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study supercritical branching processes under the influence of an i.i.d. emigration component. We provide conditions, under which the lifetime of the process is finite respectively has a finite expectation. A new version of the Kesten-Stigum theorem is obtained and the extinction probability for a large initial population size is related to the tail behaviour of the emigration.

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