S. V. Nagaev, V. I. Vakhtel', “Probability inequalities for the Galton–Watson critical process”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 266–291; Theory Probab. Appl., 50:2 (2006), 225

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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 2, Pages 266–291
DOI: https://doi.org/10.4213/tvp107 (Mi tvp107)

This article is cited in 10 scientific papers (total in 10 papers)

Probability inequalities for the Galton–Watson critical process

S. V. Nagaev^a, V. I. Vakhtel'^b

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Technische Universität München

Full-text PDF (1751 kB) Citations (10)

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DOI: https://doi.org/10.4213/tvp107

Abstract: The upper bounds for the large deviation probabilities of a critical Galton–Watson process are derived under various conditions on the offspring distribution.

Keywords: Galton–Watson process, martingale, Doob inequality, Cramèr's condition, Chebyshev inequality.

Received: 23.07.2002
Revised: 15.01.2004

English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 2, Pages 225–247
DOI: https://doi.org/10.1137/S0040585X97981640

Bibliographic databases:

Language: Russian

Citation: S. V. Nagaev, V. I. Vakhtel', “Probability inequalities for the Galton–Watson critical process”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 266–291; Theory Probab. Appl., 50:2 (2006), 225–247

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tvp107

https://doi.org/10.4213/tvp107

https://www.mathnet.ru/eng/tvp/v50/i2/p266

This publication is cited in the following 10 articles:

Dou-dou Li, Wan-lin Shi, Mei Zhang, “Large Deviations for a Critical Galton-Watson Branching Process”, Acta Math. Appl. Sin. Engl. Ser., 2024
聪彭, “Probability Inequalities for Weighted Branching Processes in Random Environments”, AAM, 13:08 (2024), 4043
Sh. K. Formanov, “Refinement of the Main Lemmas of the Theory of Critical Branching Processes”, Lobachevskii J Math, 45:7 (2024), 3290
Li D.D. Zhang M., “Asymptotic Behaviors For Critical Branching Processes With Immigration”, Acta. Math. Sin.-English Ser., 35:4 (2019), 537–549
Hautphenne S., “a Structured Markov Chain Approach To Branching Processes”, Stoch. Models, 31:3 (2015), 403–432
S. V. Nagaev, “Probability inequalities for Galton–Watson processes”, Theory Probab. Appl., 59:4 (2015), 611–640
V. I. Wachtel, D. E. Denisov, D. A. Korshunov, “Tail asymptotics for the supercritical Galton–Watson process in the heavy-tailed case”, Proc. Steklov Inst. Math., 282 (2013), 273–297
V. A. Vatutin, V. I. Vakhtel', K. Fleischmann, “Critical Galton–Watson process: The maximum of total progenies within a large window”, Theory Probab. Appl., 52:3 (2008), 470–492
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, “On probability and moment inequalities for supermartingales and martingales”, Theory Probab. Appl., 51:2 (2007), 367–377

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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