Journal of Applied Probability

Extinction probabilities of supercritical decomposable branching processes

Sophie Hautphenne

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Abstract

We focus on supercritical decomposable (reducible) multitype branching processes. Types are partitioned into irreducible equivalence classes. In this context, extinction of some classes is possible without the whole process becoming extinct. We derive criteria for the almost-sure extinction of the whole process, as well as of a specific class, conditionally given the class of the initial particle. We give sufficient conditions under which the extinction of a class implies the extinction of another class or of the whole process. Finally, we show that the extinction probability of a specific class is the minimal nonnegative solution of the usual extinction equation but with added constraints.

Article information

Source
J. Appl. Probab., Volume 49, Number 3 (2012), 639-651.

Dates
First available in Project Euclid: 6 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1346955323

Digital Object Identifier
doi:10.1239/jap/1346955323

Mathematical Reviews number (MathSciNet)
MR3012089

Zentralblatt MATH identifier
1251.60065

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Multitype branching process decomposable branching process extinction criteria extinction probability

Citation

Hautphenne, Sophie. Extinction probabilities of supercritical decomposable branching processes. J. Appl. Probab. 49 (2012), no. 3, 639--651. doi:10.1239/jap/1346955323. https://projecteuclid.org/euclid.jap/1346955323


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