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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/jsfu734
https://www.mathnet.ru/eng/jsfu/v12/i1/p51
This publication is cited in the following 2 articles:
Azam Abdurakhimovich Imomov, Erkin Egamberdievich Tukhtaev, “On asymptotic structure of critical Galton-Watson branching processes allowing immigration with infinite variance”, Stochastic Models, 39:1 (2023), 118
Azam A. Imomov, Erkin E. Tukhtaev, Applied Modeling Techniques and Data Analysis 2, 2021, 185
Citation in format AMSBIB
Contact us: