Critical Galton-Watson branching processes with a countable set of types and infinite second moments
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Published:2021-01-01
Issue:1
Volume:212
Page:1-24
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ISSN:1064-5616
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Container-title:Sbornik: Mathematics
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language:
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Short-container-title:Sb. Math.
Author:
Vatutin V. A.,Dyakonova E. E.,Topchii V. A.
Abstract
Abstract
We consider an indecomposable Galton-Watson branching process with a countable set of types. Assuming that the process is critical and may have infinite variance of the offspring sizes of some (or all) types of particles we describe the asymptotic behaviour of the survival probability of the process and establish a Yaglom-type conditional limit theorem for the infinite-dimensional vector of the number of particles of all types.
Bibliography: 20 titles.
Funder
Ministry of Science and Higher Education of the Russian Federation
Subject
Algebra and Number Theory