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Teor. Veroyatnost. i Primenen., 1981, Volume 26, Issue 4, Pages 818–824 (Mi tvp3511)  

Short Communications

On a class of limit theorems for a critical Bellman–Harris branching process

V. A. Vatutin

Moscow

Abstract: Let $z(t)$ be a critical Bellman–Harris branching process with lifetime distribution $G(t)$ and offspring generating function $f(s)=s+(1-s)^{1+\alpha}L(1-s)$, where $0<\alpha\le 1$ and $L(s)$ is slowly varying at 0. Let us denote by $f_k(s)$ the $k$-th iterate of $f(s)$. For the case when
$$ 0\le\liminf_{n\to\infty}\frac{n(1-G(n))}{1-f_n(0)}<\limsup_{n\to\infty}\frac{n(1-G(n))}{1-f_n(0)}<\infty $$
we prove some limit theorems for the process $z(t)$ which are analogous to those in [3].

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English version:
Theory of Probability and its Applications, 1982, 26:4, 806–812

Bibliographic databases:

Received: 27.03.1980

Citation: V. A. Vatutin, “On a class of limit theorems for a critical Bellman–Harris branching process”, Teor. Veroyatnost. i Primenen., 26:4 (1981), 818–824; Theory Probab. Appl., 26:4 (1982), 806–812

Citation in format AMSBIB
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\paper On a~class of limit theorems for a~critical Bellman--Harris branching process
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 4
\pages 818--824
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\zmath{https://zbmath.org/?q=an:0488.60093|0474.60067}
\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 26
\issue 4
\pages 806--812
\crossref{https://doi.org/10.1137/1126087}
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