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Teoriya Veroyatnostei i ee Primeneniya, 1977, Volume 22, Issue 1, Pages 143–149 (Mi tvp3163)  

This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

Asymptotic behaviour of the non-extinction probability for a critical branching process

V. A. Vatutin

Steklov Mathematical Institute, Academy of Sciences of the USSR, Moscow
Full-text PDF (421 kB) Citations (3)
Abstract: Critical age-dependent branching process with $k$ types $N_1,N_2,\dots,N_k$ of particles are considered. We suppose that particles' reproduction power depends on their age. Let $z_j^i(t)$ be the number of particles of type $N_j$ at time $t$ given that at time $t=0$ there was only one particle of type $N_i$. We derive an asymptotic formula for the probability $\mathbf P\{z_1^i(t)+z_2^i(t)+\dots+z_k^i(t)>0\}$ as $t\to\infty$. The result obtained is analogous to that of Goldstein [2].
Received: 14.11.1975
English version:
Theory of Probability and its Applications, 1977, Volume 22, Issue 1, Pages 140–146
DOI: https://doi.org/10.1137/1122013
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Vatutin, “Asymptotic behaviour of the non-extinction probability for a critical branching process”, Teor. Veroyatnost. i Primenen., 22:1 (1977), 143–149; Theory Probab. Appl., 22:1 (1977), 140–146
Citation in format AMSBIB
\Bibitem{Vat77}
\by V.~A.~Vatutin
\paper Asymptotic behaviour of the non-extinction probability for a~critical branching process
\jour Teor. Veroyatnost. i Primenen.
\yr 1977
\vol 22
\issue 1
\pages 143--149
\mathnet{http://mi.mathnet.ru/tvp3163}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=440723}
\zmath{https://zbmath.org/?q=an:0398.60085}
\transl
\jour Theory Probab. Appl.
\yr 1977
\vol 22
\issue 1
\pages 140--146
\crossref{https://doi.org/10.1137/1122013}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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