A special family of Galton-Watson processes with explosions

Serik Sagitov; Alexey Lindo

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arXiv · 1502.07538

A special family of Galton-Watson processes with explosions

Serik Sagitov·Alexey Lindo

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Abstract

The linear-fractional Galton-Watson processes is a well known case when many characteristics of a branching process can be computed explicitly. In this paper we extend the two-parameter linear-fractional family to a much richer four-parameter family of reproduction laws. The corresponding Galton-Watson processes also allow for explicit calculations, now with possibility for infinite mean, or even infinite number of offspring. We study the properties of this special family of branching processes, and show, in particular, that in some explosive cases the time to explosion can be approximated by the Gumbel distribution.

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Serik Sagitov, Alexey Lindo. 2015-02-26. A special family of Galton-Watson processes with explosions. https://arxiv.org/abs/1502.07538

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