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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Acknowledgements
This research was supported by the Swedish Research Council grant 621-2010-5623.
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Sagitov, S., Lindo, A. (2016). A Special Family of Galton-Watson Processes with Explosions. In: del Puerto, I., et al. Branching Processes and Their Applications. Lecture Notes in Statistics(), vol 219. Springer, Cham. https://doi.org/10.1007/978-3-319-31641-3_14
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DOI: https://doi.org/10.1007/978-3-319-31641-3_14
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