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Extinction of decomposable branching processes. (English. Russian original) Zbl 1375.60130

Discrete Math. Appl. 26, No. 3, 183-192 (2016); translation from Diskretn. Mat. 27, No. 4, 26-37 (2015).
Summary: The asymptotic behavior, as \(n\to\infty\) of the conditional distribution of the number of particles in a decomposable critical branching process \(\mathbf{Z}(m) = (Z_1(m),\dots, Z_N(m))\) with \(N\) types of particles at moment \(m = n-k\), \(k = 0(n)\), is investigated given that the extinction moment of the process equals to \(n\).

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F05 Central limit and other weak theorems
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References:

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