S. V. Nagaev, N. V. Vakhrushev, “An estimation of probabilites of large deviations for a critical Galton–Watson process”, Teor. Veroyatnost. i Primenen., 20:1 (1975), 181–182; Theory Probab. Appl., 20:1 (1975), 179

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Teoriya Veroyatnostei i ee Primeneniya, 1975, Volume 20, Issue 1, Pages 181–182 (Mi tvp3008)

This article is cited in 8 scientific papers (total in 8 papers)

Short Communications

An estimation of probabilites of large deviations for a critical Galton–Watson process

S. V. Nagaev, N. V. Vakhrushev

Novosibirsk

Full-text PDF (130 kB) Citations (8)

Abstract: Let

Z_{n}

$Z_n$ ,

n = 0, 1, \dots,

$n=0,1,\dots,$ be a critical Galton–Watson process with

Z_{0} = 1

$Z_0=1$ . An estimation of

P (Z_{n} > k)

$\mathbf P(Z_n>k)$ is obtained for every

k > 0

$k>0$ under the assumption that

P (Z_{1} > k) < e^{- α k}

$\mathbf P(Z_1>k)<e^{-\alpha k}$ ,

α > 0

$\alpha>0$ .

Received: 11.07.1974

English version:
Theory of Probability and its Applications, 1975, Volume 20, Issue 1, Pages 179–180
DOI: https://doi.org/10.1137/1120020

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: S. V. Nagaev, N. V. Vakhrushev, “An estimation of probabilites of large deviations for a critical Galton–Watson process”, Teor. Veroyatnost. i Primenen., 20:1 (1975), 181–182; Theory Probab. Appl., 20:1 (1975), 179–180

Citation in format AMSBIB

\Bibitem{NagVak75}

\by S.~V.~Nagaev, N.~V.~Vakhrushev

\paper An estimation of probabilites of large deviations for a~critical Galton--Watson process

\jour Teor. Veroyatnost. i Primenen.

\yr 1975

\vol 20

\issue 1

\pages 181--182

\mathnet{http://mi.mathnet.ru/tvp3008}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=370807}

\zmath{https://zbmath.org/?q=an:0356.60043}

\transl

\jour Theory Probab. Appl.

\yr 1975

\vol 20

\issue 1

\pages 179--180

\crossref{https://doi.org/10.1137/1120020}

Linking options:

https://www.mathnet.ru/eng/tvp3008

https://www.mathnet.ru/eng/tvp/v20/i1/p181

This publication is cited in the following 8 articles:

Ibrahim Rahimov, “Homogeneous Branching Processes with Non-Homogeneous Immigration”, Stochastics and Quality Control, 36:2 (2021), 165
Li D.D. Zhang M., “Asymptotic Behaviors For Critical Branching Processes With Immigration”, Acta. Math. Sin.-English Ser., 35:4 (2019), 537–549
Gourab Ray, “Large unicellular maps in high genus”, Ann. Inst. H. Poincaré Probab. Statist., 51:4 (2015)
S. V. Nagaev, “Probability inequalities for Galton–Watson processes”, Theory Probab. Appl., 59:4 (2015), 611–640
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, V. I. Vakhtel', “Probability inequalities for the Galton–Watson critical process”, Theory Probab. Appl., 50:2 (2006), 225–247
S. V. Nagaev, V. I. Vakhtel', “Limit theorems for probabilities of large deviations of a Galton-Watson process”, Discrete Math. Appl., 13:1 (2003), 1–26
G. D. Makarov, “Large deviations for a critical Galton–Watson process”, Theory Probab. Appl., 25:3 (1981), 481–492

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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