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On supercritical branching processes with emigration

Part of: Markov processes

Published online by Cambridge University Press:  08 July 2022

Georg Braun
Georg Braun*
Affiliation:
University of Tübingen
*
*Postal address: Mathematical Institute, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany. Email address: georg.braun@uni-tuebingen.de
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Abstract

We study supercritical branching processes under the influence of an independent and identically distributed (i.i.d.) emigration component. We provide conditions under which the lifetime of the process is finite or has a finite expectation. A theorem of Kesten–Stigum type is obtained, and the extinction probability for a large initial population size is related to the tail behaviour of the emigration.

Keywords

Extinction probabilitiesrandom difference equationautoregressive processrecurrence and transienceKesten–Stigum theorem

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 3 , September 2022 , pp. 734 - 754
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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