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

Peter Braunsteins; Geoffrey Decrouez; Sophie Hautphenne

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arXiv · 1605.03069

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

Peter Braunsteins·Geoffrey Decrouez·Sophie Hautphenne

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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 processes with countably infinitely many types. This gives rise to a number of iterative methods for the computation of the global extinction probability vector.

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Peter Braunsteins, Geoffrey Decrouez, Sophie Hautphenne. 2017-12-14. A pathwise iterative approach to the extinction of branching processes with countably many types. https://arxiv.org/abs/1605.03069

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