The survival probability of a critical multitype Galton-Watson branching process
type: Item
instance of: scholarly article
title: The survival probability of a critical multitype Galton-Watson branching process
zbMATH Open document ID: 0999.60081
DOI: 10.1023/A:1011347321909
published in: Journal of Mathematical Sciences (New York)
publication date: 2002-06-16T00:00:00Z
review text: The classical Kolmogorov theorem on the rate of decay of the probability of non-extinction in a critical branching process was recently given a probabilistic proof, sometimes also known nowadays as a conceptual proof, by \textit{J. Geiger} [J. Appl. Probab. 36, No. 2, 301-309 (1999; Zbl 0942.60071)]. This proof involves a particular decomposition of the Galton-Watson tree conditioned on survival up to a given generation. The present paper provides an analogous proof of the corresponding result for the critical multitype Galton-Watson branching process in which all family size distributions have finite variances.
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 1756317
zbMATH Keywords: Galton-Watson tree
zbMATH Keywords: conditioned limit law
zbMATH Keywords: conceptual proof
author: Vladimir Vatutin
author: Elena E. Dyakonova
reviewed by: D. R. Grey
MaRDI profile type: Publication
full work available at URL: a:1011347321909
OpenAlex ID: W116323851
description: scientific article; zbMATH DE number 1756317