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Teor. Veroyatnost. i Primenen., 1964, Volume 9, Issue 4, Pages 710–718 (Mi tvp422)  

This article is cited in 38 scientific papers (total in 38 papers)

Short Communications

Theorem on Sums of Independent Random Positive Variables and its Applications to Branching Processes

V. P. Čistyakov

Moscow

Abstract: Let $\xi_1,…,\xi_n,…$ be independent random positive variables and let ${\mathbf P}\{\xi_k<t\}=G(t)$, $k=1,…,n,…$ Let us denote
$$ {\mathbf P}\{\xi_1+…+\xi_n<t\}=G_n(t). $$

Theorem.
$$ \lim_{t\to\infty}\frac{1-G_n(t)}{1-G(t)}=n,\qquad n=1,2,3,…, $$
and only if
$$ \lim_{t\to\infty}\frac{1-G_2(t)}{1-G(t)}=2. $$
This theorem is useful in some investigations of age-dependent branching processes.

Full text: PDF file (448 kB)

English version:
Theory of Probability and its Applications, 1964, 9:4, 640–648

Bibliographic databases:

Received: 07.01.1964

Citation: V. P. Čistyakov, “Theorem on Sums of Independent Random Positive Variables and its Applications to Branching Processes”, Teor. Veroyatnost. i Primenen., 9:4 (1964), 710–718; Theory Probab. Appl., 9:4 (1964), 640–648

Citation in format AMSBIB
\Bibitem{Chi64}
\by V.~P.~{\v C}istyakov
\paper Theorem on Sums of Independent Random Positive Variables and its Applications to Branching Processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1964
\vol 9
\issue 4
\pages 710--718
\mathnet{http://mi.mathnet.ru/tvp422}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=170394}
\zmath{https://zbmath.org/?q=an:0203.19401}
\transl
\jour Theory Probab. Appl.
\yr 1964
\vol 9
\issue 4
\pages 640--648
\crossref{https://doi.org/10.1137/1109088}


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    Citing articles on Google Scholar: Russian citations, English citations
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