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Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 2, Pages 296–309 (Mi tvp2534)  

This article is cited in 1 scientific paper (total in 1 paper)

A condition of degeneracy of a bounded branching process with continuous time

A. M. Zubkov

Moscow

Abstract: We consider a bounded branching process with continuous time, i.e. a supercritical branching process with the condition that at any moment the number of particles is bounded from above (the “superfluous” particles are destroyed and have no offspring). A necessary and sufficient condition is given for the process to die (to get into the state when there is no particle at all) with probability one. We find that the “critical levels” of the upper bound are slightly different for discrete and continuous time.

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English version:
Theory of Probability and its Applications, 1973, 17:2, 284–297

Bibliographic databases:

Received: 30.12.1971

Citation: A. M. Zubkov, “A condition of degeneracy of a bounded branching process with continuous time”, Teor. Veroyatnost. i Primenen., 17:2 (1972), 296–309; Theory Probab. Appl., 17:2 (1973), 284–297

Citation in format AMSBIB
\Bibitem{Zub72}
\by A.~M.~Zubkov
\paper A~condition of degeneracy of a~bounded branching process with continuous time
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 2
\pages 296--309
\mathnet{http://mi.mathnet.ru/tvp2534}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=300352}
\zmath{https://zbmath.org/?q=an:0279.60081}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 17
\issue 2
\pages 284--297
\crossref{https://doi.org/10.1137/1117032}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. K. Kobanenko, “Predelnye teoremy dlya ogranichennykh vetvyaschikhsya protsessov”, Diskret. matem., 29:2 (2017), 18–28  mathnet  crossref  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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