Limit theorems for the total number of descendants for the Galton--Watson branching process
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 503-528
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The main results of the present paper deal with the asymptotic behavior of the conditional distribution for the whole number of descendants $S_n $ of a single particle in the Galton–Watson process with respect to the condition that the process degenerates at time n and the expectation for the number of particles generated by one particle tends to 1 as $n \to \infty $.
Keywords:
the Galton–Watson branching processes, processes close to critical ones, degeneracy, asymptotic behavior of the total number of descendants.
@article{TVP_1993_38_3_a2,
author = {A. V. Karpenko and S. V. Nagaev},
title = {Limit theorems for the total number of descendants for the {Galton--Watson} branching process},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {503--528},
publisher = {mathdoc},
volume = {38},
number = {3},
year = {1993},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a2/}
}
TY - JOUR AU - A. V. Karpenko AU - S. V. Nagaev TI - Limit theorems for the total number of descendants for the Galton--Watson branching process JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1993 SP - 503 EP - 528 VL - 38 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a2/ LA - ru ID - TVP_1993_38_3_a2 ER -
%0 Journal Article %A A. V. Karpenko %A S. V. Nagaev %T Limit theorems for the total number of descendants for the Galton--Watson branching process %J Teoriâ veroâtnostej i ee primeneniâ %D 1993 %P 503-528 %V 38 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a2/ %G ru %F TVP_1993_38_3_a2
A. V. Karpenko; S. V. Nagaev. Limit theorems for the total number of descendants for the Galton--Watson branching process. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 503-528. http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a2/