Abstract:
Let $\left\{ Z_{i},\text{ }i=0,1,\ldots \right\} $ be a strongly supercritical branching process in a random environment. It is assumed that the reproduction laws of particles in different generations are geometric. Let $T$ be the extinction time of the specified process. It is shown that the coordinates of a random vector $\left( Z_{0},Z_{1},\ldots ,Z_{n}\right)$ with numbers distant from each other and from $0$ and $n$ are asymptotically independent, provided that $n<T<+\infty $, $n\rightarrow \infty $, and have the same limiting distribution.
Keywords:strongly supercritical branching process in a random environment, conditional limit theorems.
The work was supported by the Russian Science Foundation under grant no.19-11-00111-П, https://rscf.ru/en/project/19-11-00111/, and performed at Steklov Mathematical Institute of Russian Academy of Sciences.
Received: 30.11.2023
Document Type:
Article
UDC:519.218.2
Language: Russian
Citation:
V. I. Afanasyev, “Strongly supercritical branching process in a random environment dying at a distant moment”, Diskr. Mat., 36:1 (2024), 3–14
\Bibitem{Afa24}
\by V.~I.~Afanasyev
\paper Strongly supercritical branching process in a random environment dying at a distant moment
\jour Diskr. Mat.
\yr 2024
\vol 36
\issue 1
\pages 3--14
\mathnet{http://mi.mathnet.ru/dm1807}
\crossref{https://doi.org/10.4213/dm1807}