Critical branching populations with reproductive sibling correlations
type: Item
instance of: scholarly article
title: Critical branching populations with reproductive sibling correlations
zbMATH Open document ID: 0657.60109
DOI: 10.1016/0304-4149(88)90080-4
author: Per Broberg
published in: Stochastic Processes and their Applications
publication date: 1988-01-01T00:00:00Z
review text: The classical Galton-Watson process is modified to allow the possibility that if two individuals are siblings (have a common parent in the previous generation) then their family sizes may be dependent, although retaining a constant marginal distribution. In the critical case where this distribution has mean one, analogues of the Yaglom limit laws are obtained. The technique used is to compare with the embedded process of only children, which is a critical Galton-Watson process. An extension to the general branching process is also obtained relying on results of an unpublished report by Nerman.
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 4074147
zbMATH Keywords: embedding
zbMATH Keywords: Galton-Watson process
zbMATH Keywords: siblings
zbMATH Keywords: critical
zbMATH Keywords: general branching process
reviewed by: D. R. Grey
MaRDI profile type: Publication
full work available at URL: 0304-4149(88)90080-4
OpenAlex ID: W2076624259
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description: scientific article; zbMATH DE number 4074147