Geodesic
Strongly supercritical branching process in a random environment dying at a distant moment
Diskretnaya Matematika, Tome 36 (2024) no. 1, pp. 3-14 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $n$, $n\rightarrow \infty $, and have the same limiting distribution.
Keywords: strongly supercritical branching process in a random environment, conditional limit theorems. 
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V. I. Afanasyev. Strongly supercritical branching process in a random environment dying at a distant moment. Diskretnaya Matematika, Tome 36 (2024) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/DM_2024_36_1_a0/

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