A special family of Galton-Watson processes with explosions
Kapitel i bok, 2016

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.

Författare

Serik Sagitov

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematisk statistik

Alexey Lindo

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematisk statistik

Lecture Notes in Statistics, Workshop on Branching Processes and their Applications, WBPA 2015, Badajoz, Spain, 7-10 April 2015

237-254

Fundament

Grundläggande vetenskaper

Ämneskategorier

Sannolikhetsteori och statistik

DOI

10.1007/978-3-319-31641-3_14

Mer information

Senast uppdaterat

2021-06-28