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This article is cited in 10 scientific papers (total in 10 papers)
On the time of reaching a fixed level by a critical branching process in a random environment
V. I. Afanasyev
Abstract:
Let $\{\xi_n\}$ be a critical branching process in a random environment
with linear-fractional generating functions; let
$T$ be the extinction time of $\{\xi_n\}$, and $T_x$ be the
time of first passage of the semiaxis $(x,\infty)$.
We find the asymptotic distributions of the random variables
$T_x/\ln^2 x$, $T_x/T$, $T/\ln^2x$ under the condition $\{T_x<\infty\}$ as $x\to \infty$.
DOI:
https://doi.org/10.4213/dm390
 Full text:
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English version:
Discrete Mathematics and Applications, 1999, 9:6, 627–643
Bibliographic databases:
 
UDC:
519.2
Received: 03.07.1998
Citation:
V. I. Afanasyev, “On the time of reaching a fixed level by a critical branching process in a random environment”, Diskr. Mat., 11:4 (1999), 33–47; Discrete Math. Appl., 9:6 (1999), 627–643
Citation in format AMSBIB
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\by V.~I.~Afanasyev
\paper On the time of reaching a fixed level by a critical branching process in a random environment
\jour Diskr. Mat.
\yr 1999
\vol 11
\issue 4
\pages 33--47
\mathnet{http://mi.mathnet.ru/dm390}
\crossref{https://doi.org/10.4213/dm390}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1761010}
\zmath{https://zbmath.org/?q=an:0971.60087}
\transl
\jour Discrete Math. Appl.
\yr 1999
\vol 9
\issue 6
\pages 627--643
Linking options:
http://mi.mathnet.ru/eng/dm390https://doi.org/10.4213/dm390 http://mi.mathnet.ru/eng/dm/v11/i4/p33
Citing articles on Google Scholar:
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Russian articles,
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This publication is cited in the following articles:
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V. I. Afanasyev, “On the time of attaining a maximum by a critical branching process in a random environment and by a stopped random walk”, Discrete Math. Appl., 10:3 (2000), 243–264
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V. I. Afanasyev, “On the ratio between the maximal and
total numbers of individuals in
a critical branching process in a random environment”, Theory Probab. Appl., 48:3 (2004), 384–399
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V. I. Afanasyev, “Arcsine law for branching processes in a random environment and Galton–Watson processes”, Theory Probab. Appl., 51:3 (2007), 401–414
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V. I. Afanasyev, “Invariance Principle for the Critical Branching Process in a Random Environment Attaining a High Level”, Theory Probab. Appl., 54:1 (2010), 1–13
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V. I. Afanasyev, “Brownian high jump”, Theory Probab. Appl., 55:2 (2011), 183–197
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Afanasyev V.I., “New Invariance Principles for Critical Branching Process in Random Environment”, Advances in Data Analysis - Theory and Applications to Reliability and Inference, Data Mining, Bioinformatics, Lifetime Data, and Neural Networks, Statistics for Industry and Technology, 2010, 105–115
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V. I. Afanasyev, “High level subcritical branching processes in a random environment”, Proc. Steklov Inst. Math., 282 (2013), 4–14
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V. I. Afanasyev, “Conditional limit theorem for maximum of random walk in a random environment”, Theory Probab. Appl., 58:4 (2014), 525–545
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V. I. Afanasyev, “Functional limit theorem for a stopped random walk attaining a high level”, Discrete Math. Appl., 27:5 (2017), 269–276
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Vatutin V., Dyakonova E., “Path to Survival For the Critical Branching Processes in a Random Environment”, J. Appl. Probab., 54:2 (2017), 588–602
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