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

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

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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• https://doi.org/10.4213/dm183
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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
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
3. S. V. Nagaev, “Probability inequalities for Galton–Watson processes”, Theory Probab. Appl., 59:4 (2015), 611–640
4. Li D.D., Zhang M., “Asymptotic Behaviors For Critical Branching Processes With Immigration”, Acta. Math. Sin.-English Ser., 35:4 (2019), 537–549
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