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Sbornik: Mathematics, 2021, Volume 212, Issue 1, Pages 1–24
DOI: https://doi.org/10.1070/SM9402 (Mi sm9402) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Critical Galton-Watson branching processes with a countable set of types and infinite second moments

V. A. Vatutina, E. E. Dyakonovaa, V. A. Topchiibc

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Mathematical Center in Akademgorodok, Novosibirsk
c Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
English version PDF (591 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM9402
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.
Keywords: critical Galton-Watson branching processes with a countable set of types, survival probability, infinite second moments of offspring sizes, regularly varying functions, Yaglom-type limit theorem.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1614
075-15-2019-1613
The work of V. A. Vatutin and E. E. Dyakonova was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2019-1614). The work of V. A. Topchii was performed at the Mathematical Center in Akademgorodok, Novosibirsk, and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2019-1613).
Received: 02.03.2020 and 29.05.2020
Russian version:
Matematicheskii Sbornik, 2021, Volume 212, Number 1, Pages 3–27
DOI: https://doi.org/10.4213/sm9402
Bibliographic databases:
Document Type: Article
UDC: 519.218.23+519.217.2
MSC: Primary 60J80; Secondary 60B12, 60J10
Language: English
Original paper language: Russian
Citation: V. A. Vatutin, E. E. Dyakonova, V. A. Topchii, “Critical Galton-Watson branching processes with a countable set of types and infinite second moments”, Mat. Sb., 212:1 (2021), 3–27; Sb. Math., 212:1 (2021), 1–24
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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