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Diskretnaya Matematika, 2003, Volume 15, Issue 1, Pages 3–27
DOI: https://doi.org/10.4213/dm183 (Mi dm183) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Limit theorems for probabilities of large deviations of a Galton-Watson process

S. V. Nagaev, V. I. Vakhtel'
Full-text PDF (1433 kB) Citations (6)
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DOI: https://doi.org/10.4213/dm183
Abstract: We prove local and integral limit theorems for large deviations of Cramer type for a critical Galton–Watson branching process under the assumption that the radius of convergence of the generating function of the progeny is strictly greater than one. The proof is based on a modified Cramer approach which consists of construction of an auxiliary non-homogeneous in time branching process.
This research was supported by the Russian Foundation for Basic Research, grant 02–01–01252, and by INTAS, grants 99–01317, 00–265.
Received: 29.04.2002
English version:
Discrete Mathematics and Applications, 2003, Volume 13, Issue 1, Pages 1–26
DOI: https://doi.org/10.1515/156939203321669537
Bibliographic databases:
UDC: 519.2
Language: Russian
Citation: S. V. Nagaev, V. I. Vakhtel', “Limit theorems for probabilities of large deviations of a Galton-Watson process”, Diskr. Mat., 15:1 (2003), 3–27; Discrete Math. Appl., 13:1 (2003), 1–26
Citation in format AMSBIB
\Bibitem{NagWac03}
\by S.~V.~Nagaev, V.~I.~Vakhtel'
\paper Limit theorems for probabilities of large deviations of a Galton-Watson process
\jour Diskr. Mat.
\yr 2003
\vol 15
\issue 1
\pages 3--27
\mathnet{http://mi.mathnet.ru/dm183}
\crossref{https://doi.org/10.4213/dm183}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1996743}
\zmath{https://zbmath.org/?q=an:1102.60316}
\transl
\jour Discrete Math. Appl.
\yr 2003
\vol 13
\issue 1
\pages 1--26
\crossref{https://doi.org/10.1515/156939203321669537}
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    • This publication is cited in the following 6 articles:
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