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 Mat. Zametki: Year: Volume: Issue: Page: Find

 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 $T=0$.

Full text: PDF file (608 kB)

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

Bibliographic databases:

UDC: 519.2

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}