A special family of Galton-Watson processes with explosions
Book chapter, 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.

Author

Serik Sagitov

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Alexey Lindo

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Lecture Notes in Statistics

0930-0325 (ISSN) 2197-7186 (eISSN)

Vol. 219 237-254
978-331931639-0 (ISBN)

Roots

Basic sciences

Subject Categories

Probability Theory and Statistics

DOI

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

More information

Latest update

7/11/2024