General linear-fractional branching processes with discrete time.
Journal article, 2018

We study a linear-fractional Bienayme-Galton-Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads to the linear-fractional distribution formula for an arbitrary observation time, which allows us to establish transparent limit theorems for the subcritical, critical and supercritical cases. Our results extend recent findings for the linear-fractional branching processes with countably many types.

Crump-Mode-Jagers process

Bienayme-Galton-Watson process with a general type space

General linear-fractional distribution

general Markov chains and irreducible kernels


Alexey Lindo

Mathematical Statistics

University of Gothenburg

Serik Sagitov

University of Gothenburg

Chalmers, Mathematical Sciences


1744-2508 (ISSN) 1744-2516 (eISSN)

Vol. 90 3 364-378

Subject Categories


Computational Mathematics

Probability Theory and Statistics

Control Engineering

Mathematical Analysis

Areas of Advance

Life Science Engineering (2010-2018)



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Latest update

3/5/2020 1