General linear-fractional branching processes with discrete time.
Artikel i vetenskaplig tidskrift, 2015

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.

general Markov chains and irreducible kernels

Bienayme-Galton-Watson process with a general type space

General linear-fractional distribution

Crump-Mode-Jagers process

Författare

Alexey Lindo

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Serik Sagitov

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Stochastics

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

Vol. 90 364-378

Ämneskategorier

Matematik

Beräkningsmatematik

Sannolikhetsteori och statistik

Reglerteknik

Matematisk analys

Styrkeområden

Livsvetenskaper och teknik

DOI

10.1080/17442508.2017.1357722