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December 2013 Extinction probabilities of branching processes with countably infinitely many types
S. Hautphenne, G. Latouche, G. Nguyen
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Adv. in Appl. Probab. 45(4): 1068-1082 (December 2013). DOI: 10.1239/aap/1386857858

Abstract

We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated Galton-Watson processes with finite sets of types and modified progeny generating functions. In addition, we discuss the connection of the convergence norm of the mean progeny matrix with extinction criteria. Finally, we give a sufficient condition for a population to become extinct almost surely even though its population size explodes on the average, which is impossible in a branching process with finitely many types. We conclude with some numerical illustrations for our algorithmic methods.

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S. Hautphenne. G. Latouche. G. Nguyen. "Extinction probabilities of branching processes with countably infinitely many types." Adv. in Appl. Probab. 45 (4) 1068 - 1082, December 2013. https://doi.org/10.1239/aap/1386857858

Information

Published: December 2013
First available in Project Euclid: 12 December 2013

zbMATH: 1287.60102
MathSciNet: MR3161297
Digital Object Identifier: 10.1239/aap/1386857858

Subjects:
Primary: 60J80
Secondary: 60J05, 60J22, 65H10

Rights: Copyright © 2013 Applied Probability Trust

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Vol.45 • No. 4 • December 2013
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