A pathwise approach to the extinction of branching processes with countably many types

Peter Braunsteins, Geoffrey Decrouez and Sophie Hautphenne

Stochastic Processes and their Applications, 2019, vol. 129, issue 3, 713-739

Abstract: We consider the extinction events of Galton–Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton–Watson processes with finite but increasing sets of types. A pathwise approach is then used to show that, under some sufficient conditions, the corresponding sequence of extinction probability vectors converges to the global extinction probability vector of the Galton–Watson process with countably infinitely many types. Besides giving rise to a family of new iterative methods for computing the global extinction probability vector, our approach paves the way to new global extinction criteria for branching processes with countably infinitely many types.

Keywords: Multitype branching process; Extinction probability; Pathwise approach; Extinction criterion (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.03.013

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