|
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
Full text:
PDF file (1433 kB)
References:
PDF file
HTML file
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}
Linking options:
http://mi.mathnet.ru/eng/dm183https://doi.org/10.4213/dm183 http://mi.mathnet.ru/eng/dm/v15/i1/p3
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
S. V. Nagaev, V. I. Vakhtel', “Probability inequalities for the Galton–Watson critical process”, Theory Probab. Appl., 50:2 (2006), 225–247
-
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
-
S. V. Nagaev, “Probability inequalities for Galton–Watson processes”, Theory Probab. Appl., 59:4 (2015), 611–640
-
Li D.D., Zhang M., “Asymptotic Behaviors For Critical Branching Processes With Immigration”, Acta. Math. Sin.-English Ser., 35:4 (2019), 537–549
|
Number of views: |
This page: | 343 | Full text: | 182 | References: | 40 | First page: | 1 |
|