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Diskr. Mat., 2003, Volume 15, Issue 1, Pages 3–27 (Mi dm183)  

This article is cited in 4 scientific papers (total in 4 papers)

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

S. V. Nagaev, V. I. Vakhtel'


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.

DOI: https://doi.org/10.4213/dm183

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English version:
Discrete Mathematics and Applications, 2003, 13:1, 1–26

Bibliographic databases:

UDC: 519.2
Received: 29.04.2002

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{NagVak03}
\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://www.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 articles:
    1. S. V. Nagaev, V. I. Vakhtel', “Probability inequalities for the Galton–Watson critical process”, Theory Probab. Appl., 50:2 (2006), 225–247  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. I. Vakhtel', “Limit Theorems for Probabilities of Large Deviations of a Critical Galton–Watson Process Having Power Tails”, Theory Probab. Appl., 52:4 (2008), 674–688  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. V. Nagaev, “Probability inequalities for Galton–Watson processes”, Theory Probab. Appl., 59:4 (2015), 611–640  mathnet  crossref  crossref  isi  elib
    4. Li D.D., Zhang M., “Asymptotic Behaviors For Critical Branching Processes With Immigration”, Acta. Math. Sin.-English Ser., 35:4 (2019), 537–549  crossref  mathscinet  zmath  isi  scopus
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