Linear-fractional branching processes with countably many types
Artikel i vetenskaplig tidskrift, 2013

We study multi-type Bienayme-Galton-Watson processes with linear-fractional reproduction laws using various analytical tools like the contour process, spinal representation, Perron-Frobenius theorem for countable matrices, and renewal theory. For this special class of branching processes with countably many types we present a transparent criterion for R-positive recurrence with respect to the type space. This criterion appeals to the Malthusian parameter and the mean age at childbearing of the associated linear-fractional Crump-Mode-Jagers process.

Crump-Mode-Jagers process

Renewal theory

Bienayme-Galton-Watson process

R-positive recurrence

Perron-Frobenius theorem

Spinal representation

Malthusian parameter

Contour process

Multivariate linear-fractional distribution


Serik Sagitov

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematisk statistik

Stochastic Processes and their Applications

0304-4149 (ISSN)

Vol. 123 8 2940-2956

Stokastiska modeller av gen- och artträd

Vetenskapsrådet (VR) (2010-5623), 2011-01-01 -- 2013-12-31.


Sannolikhetsteori och statistik



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