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Journal of Siberian Federal University. Mathematics & Physics, 2019, Volume 12, Issue 1, Pages 51–57
DOI: https://doi.org/10.17516/1997-1397-2019-12-1-51-57 (Mi jsfu734) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On application of slowly varying functions with remainder in the theory of Galton–Watson branching process

Azam A. Imomovab, Erkin E. Tukhtaeva

a Karshi State University, 17, Kuchabag st., Karshi city, 180100, Uzbekistan
b State Testing Center under the Cabinet of Ministers of the Republic of Uzbekistan, 12, Bogishamol st., 100202, Tashkent
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DOI: https://doi.org/10.17516/1997-1397-2019-12-1-51-57
Abstract: We investigate an application of slowly varying functions (in sense of Karamata) in the theory of Galton–Watson branching processes. Consider the critical case so that the generating function of the per-capita offspring distribution has the infinite second moment, but its tail is regularly varying with remainder. We improve the Basic Lemma of the theory of critical Galton-Watson branching processes and refine some well-known limit results.
Keywords: Galton–Watson branching process, slowly varying functions, generating functions.
Received: 27.06.2018
Received in revised form: 17.08.2018
Accepted: 07.10.2018
Bibliographic databases:
Document Type: Article
UDC: 519.218.2
Language: English
Citation: Azam A. Imomov, Erkin E. Tukhtaev, “On application of slowly varying functions with remainder in the theory of Galton–Watson branching process”, J. Sib. Fed. Univ. Math. Phys., 12:1 (2019), 51–57
Citation in format AMSBIB
\Bibitem{ImoTuk19}
\by Azam~A.~Imomov, Erkin~E.~Tukhtaev
\paper On application of slowly varying functions with remainder in the theory of Galton--Watson branching process
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 1
\pages 51--57
\mathnet{http://mi.mathnet.ru/jsfu734}
\crossref{https://doi.org/10.17516/1997-1397-2019-12-1-51-57}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000458446400004}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал Сибирского федерального университета. Серия "Математика и физика"
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