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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 2, Pages 266–291 (Mi tvp107)  

This article is cited in 7 scientific papers (total in 7 papers)

Probability inequalities for the Galton–Watson critical process

S. V. Nagaeva, V. I. Vakhtel'b

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

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.

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

Full text: PDF file (1751 kB)
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English version:
Theory of Probability and its Applications, 2006, 50:2, 225–247

Bibliographic databases:

Received: 23.07.2002
Revised: 15.01.2004

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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    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:
    1. S. V. Nagaev, “On probability and moment inequalities for supermartingales and martingales”, Theory Probab. Appl., 51:2 (2007), 367–377  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    3. 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
    4. 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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. S. V. Nagaev, “Probability inequalities for Galton–Watson processes”, Theory Probab. Appl., 59:4 (2015), 611–640  mathnet  crossref  crossref  isi  elib
    6. Hautphenne S., “a Structured Markov Chain Approach To Branching Processes”, Stoch. Models, 31:3 (2015), 403–432  crossref  mathscinet  zmath  isi  elib  scopus
    7. 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
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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