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 Teor. Veroyatnost. i Primenen., 1969, Volume 14, Issue 2, Pages 348–354 (Mi tvp1182)

Short Communications

Some explicit formulas in the theory of branching stochastic processes with discrete time and one-type particles

B. I. Selivanov

Moscow

Abstract: Let $Z_0=1$, $Z_n$, $n=1,2,…,$ be the number of particles belonging to the $n$-th generation of a Halton–Watson branching process, $p_{nr}=\mathbf PŻ_n=r\}$ and $F_n(z)=\sum_{r\ge0}p_{nr}z^r$. It is supposed that $m=\mathbf EZ_1\ne1$ and $F(z)=F_1(z)$ be regular at the point $z=1$ for $m<1$. In the paper some formulas and an asymptotic expansion for the probabilities $p_{nr}$ are obtained.

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English version:
Theory of Probability and its Applications, 1969, 14:2, 336–342

Bibliographic databases:

Revised: 24.01.1968

Citation: B. I. Selivanov, “Some explicit formulas in the theory of branching stochastic processes with discrete time and one-type particles”, Teor. Veroyatnost. i Primenen., 14:2 (1969), 348–354; Theory Probab. Appl., 14:2 (1969), 336–342

Citation in format AMSBIB
\Bibitem{Sel69} \by B.~I.~Selivanov \paper Some explicit formulas in the theory of branching stochastic processes with discrete time and one-type particles \jour Teor. Veroyatnost. i Primenen. \yr 1969 \vol 14 \issue 2 \pages 348--354 \mathnet{http://mi.mathnet.ru/tvp1182} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=246378} \zmath{https://zbmath.org/?q=an:0281.60100|0214.16301} \transl \jour Theory Probab. Appl. \yr 1969 \vol 14 \issue 2 \pages 336--342 \crossref{https://doi.org/10.1137/1114043}