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Mat. Zametki, 1975, Volume 18, Issue 1, Pages 123–128 (Mi mz7633)  

Limit theorem for a supercritical Galton–Watson process

I. S. Badalbaev

Mathematical Institute, Academy of Sciences of Uzbek SSR

Abstract: Let $\mu_n$, $n=0,1,…$ be a Galton–Watson process, and $\tau_x+1$ the instant of first crossing of the level $x$ by the process. A limit theorem is proved for the joint distribution of the random variables
$$ \tau_x,\quad x-\mu_{\tau_x},\quad\mu_{\tau_x+1}-x\quad(x\to\infty) $$
on the assumption that $M\mu_1\ln(1+\mu_1)<\infty$.

Full text: PDF file (293 kB)

English version:
Mathematical Notes, 1975, 18:1, 656–659

Bibliographic databases:

UDC: 519.2
Received: 20.08.1973

Citation: I. S. Badalbaev, “Limit theorem for a supercritical Galton–Watson process”, Mat. Zametki, 18:1 (1975), 123–128; Math. Notes, 18:1 (1975), 656–659

Citation in format AMSBIB
\Bibitem{Bad75}
\by I.~S.~Badalbaev
\paper Limit theorem for a~supercritical Galton--Watson process
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 1
\pages 123--128
\mathnet{http://mi.mathnet.ru/mz7633}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=397910}
\zmath{https://zbmath.org/?q=an:0335.60053}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 1
\pages 656--659
\crossref{https://doi.org/10.1007/BF01461149}


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