This article is cited in 14 papers

Decomposable branching processes with a fixed extinction moment

V. A. Vatutin, E. E. D'yakonova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: The asymptotic behavior as $n\to \infty $ of the probability of the event that a decomposable critical branching process $\mathbf Z(m)= (Z_1(m),\dots ,Z_N(m))$, $m=0,1,2,\dots $, with $N$ types of particles dies at moment $n$ is investigated, and conditional limit theorems are proved that describe the distribution of the number of particles in the process $\mathbf Z(\cdot )$ at moment $m<n$ given that the extinction moment of the process is $n$. These limit theorems can be considered as statements describing the distribution of the number of vertices in the layers of certain classes of simply generated random trees of fixed height.

UDC: 519.218.24

Received: March 15, 2015

DOI: 10.1134/S0371968515030103

 English version: Proceedings of the Steklov Institute of Mathematics, 2015, 290:1, 103–124

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