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Teoriya Veroyatnostei i ee Primeneniya, 1983, Volume 28, Issue 3, Pages 458–467 (Mi tvp2190)  

This article is cited in 4 scientific papers (total in 4 papers)

The life-periods of critical branching processes with random migration

N. M. Yanev, K. V. Mitov

Sofia, Bulgaria
Full-text PDF (515 kB) Citations (4)
Abstract: Let $\{\xi_{ij}(t)\}_{j,t=1}^\infty$ ($i=1,2$), $\{\eta_t\}_{t=1}^\infty$ be independent integer-valued random variables with $F_i(s)=\mathbf Es^{\xi_{ij}(t)}$,
$$ \mathbf P\{\eta_t=-1\}=p,\ \mathbf P\{\eta_t=0\}=q,\ \mathbf P\{\eta_t=1\}=r,\ p+q+r=1. $$
The branching process with random migration $\mu_t$ is defined by the following formula: if $\mu_t=n$ then
$$ \mu_{t+1}=\sum_{j=1}^{\varphi_1(t;n)}\xi_{1j}(t+1)+\sum_{j=1}^{\varphi_2(t;n)}\xi_{2j}(t+1),\quad t=0,1,\dots, $$
where $\varphi_1(t;n)=\max\{\min\{n,n+\eta_t\},0\}$, $\varphi_2(t;n)=\max\{0,\eta_t\}$. In the critical case ($F'_1(1)=1$) we investigate the asymptotical behaviour of the probability $\mathbf P\{\tau>t\}$, $t\to\infty$, where $\tau$ is the life-period defined by the conditions $\mu_{T-1}=0$, $\mu_t>0\,(T\le t<T+\tau)$, $\mu_{T+\tau}=0$.
Received: 05.02.1980
English version:
Theory of Probability and its Applications, 1984, Volume 28, Issue 3, Pages 481–491
DOI: https://doi.org/10.1137/1128045
Bibliographic databases:
Language: Russian
Citation: N. M. Yanev, K. V. Mitov, “The life-periods of critical branching processes with random migration”, Teor. Veroyatnost. i Primenen., 28:3 (1983), 458–467; Theory Probab. Appl., 28:3 (1984), 481–491
Citation in format AMSBIB
\Bibitem{YanMit83}
\by N.~M.~Yanev, K.~V.~Mitov
\paper The life-periods of critical branching processes with random migration
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 3
\pages 458--467
\mathnet{http://mi.mathnet.ru/tvp2190}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=716304}
\zmath{https://zbmath.org/?q=an:0543.60084|0511.60077}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 3
\pages 481--491
\crossref{https://doi.org/10.1137/1128045}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984SY24800002}
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  • https://www.mathnet.ru/eng/tvp/v28/i3/p458
  • This publication is cited in the following 4 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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