Diskretnaya Matematika, Tome 10 (1998) no. 3, pp. 131-147
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V. I. Afanasyev. A functional limit theorem for the logarithm of a moderately subcritical branching process in a random environment. Diskretnaya Matematika, Tome 10 (1998) no. 3, pp. 131-147. http://geodesic.mathdoc.fr/item/DM_1998_10_3_a10/
@article{DM_1998_10_3_a10,
author = {V. I. Afanasyev},
title = {A functional limit theorem for the logarithm of a moderately subcritical branching process in a random environment},
journal = {Diskretnaya Matematika},
pages = {131--147},
year = {1998},
volume = {10},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1998_10_3_a10/}
}
TY - JOUR
AU - V. I. Afanasyev
TI - A functional limit theorem for the logarithm of a moderately subcritical branching process in a random environment
JO - Diskretnaya Matematika
PY - 1998
SP - 131
EP - 147
VL - 10
IS - 3
UR - http://geodesic.mathdoc.fr/item/DM_1998_10_3_a10/
LA - ru
ID - DM_1998_10_3_a10
ER -
%0 Journal Article
%A V. I. Afanasyev
%T A functional limit theorem for the logarithm of a moderately subcritical branching process in a random environment
%J Diskretnaya Matematika
%D 1998
%P 131-147
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/DM_1998_10_3_a10/
%G ru
%F DM_1998_10_3_a10
Let $\{\xi_n\}$ be a moderately subcritical branching process in a random environment with linear-fractional generating functions. We prove that, as $n\to\infty$, the sequence of stochastic processes $\{\ln\xi_{[nt]}/(\Delta \sqrt n),\ t\in [0,1]\mid \xi_n>0\}$, where $\Delta$ is some positive constant, converges in distribution to the Brownian excursion $\{W_0^+(t),\ t\in [0,1]\}$ in the space $D[0,1]$ with Skorokhod topology.
