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Mat. Zametki, 1977, Volume 21, Issue 5, Pages 727–736 (Mi mz8003)  

A conditional limit theorem for a critical Branching process with immigration

V. A. Vatutin

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: The life period of a branching process with immigration begins at the moment $T$ and has length $\tau$ if the number of particles $\mu(T-0)=0$, $\mu(t)>0$ for all $T\le t<T+\tau$, $\mu(T+\tau)=0$ (the trajectories of the process are assumed to be continuous from the right). For a critical Markov branching process is obtained a limit theorem on the behavior of $\mu(t)$ under the condition that $\tau>t$ and $T=0$.

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English version:
Mathematical Notes, 1977, 21:5, 405–411

Bibliographic databases:

UDC: 519.2
Received: 16.02.1976

Citation: V. A. Vatutin, “A conditional limit theorem for a critical Branching process with immigration”, Mat. Zametki, 21:5 (1977), 727–736; Math. Notes, 21:5 (1977), 405–411

Citation in format AMSBIB
\Bibitem{Vat77}
\by V.~A.~Vatutin
\paper A~conditional limit theorem for a~critical Branching process with immigration
\jour Mat. Zametki
\yr 1977
\vol 21
\issue 5
\pages 727--736
\mathnet{http://mi.mathnet.ru/mz8003}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=451433}
\zmath{https://zbmath.org/?q=an:0411.60081}
\transl
\jour Math. Notes
\yr 1977
\vol 21
\issue 5
\pages 405--411
\crossref{https://doi.org/10.1007/BF01788239}


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