General linear-fractional branching processes with discrete time

Lindo, A. and Sagitov, S. (2018) General linear-fractional branching processes with discrete time. Stochastics, 90(3), pp. 364-378. (doi:10.1080/17442508.2017.1357722)

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Abstract

We study a linear-fractional Bienaymé–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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Lindo, Dr Alexey
Authors: Lindo, A., and Sagitov, S.
College/School:College of Science and Engineering > School of Mathematics and Statistics
Journal Name:Stochastics
Publisher:Taylor & Francis
ISSN:1744-2508
ISSN (Online):1744-2516
Published Online:02 August 2017

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