We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the gaussian and the purely non-gaussian parts of the infinitely divisible limit. We also discuss the rate of Poisson convergence and emphasize the special case of Bernoulli random variables. The proofs are mainly based on Lindeberg's method.
Mots-clés : infinitely divisible distributions, Lévy processes, weak dependence, association, binary random variables, number of exceedances
@article{PS_2005__9__38_0,
author = {Dedecker, J\'er\^ome and Louhichi, Sana},
title = {Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences},
journal = {ESAIM: Probability and Statistics},
pages = {38--73},
publisher = {EDP-Sciences},
volume = {9},
year = {2005},
doi = {10.1051/ps:2005003},
mrnumber = {2148960},
zbl = {1136.60308},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2005003/}
}
TY - JOUR AU - Dedecker, Jérôme AU - Louhichi, Sana TI - Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences JO - ESAIM: Probability and Statistics PY - 2005 SP - 38 EP - 73 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2005003/ DO - 10.1051/ps:2005003 LA - en ID - PS_2005__9__38_0 ER -
%0 Journal Article %A Dedecker, Jérôme %A Louhichi, Sana %T Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences %J ESAIM: Probability and Statistics %D 2005 %P 38-73 %V 9 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2005003/ %R 10.1051/ps:2005003 %G en %F PS_2005__9__38_0
Dedecker, Jérôme; Louhichi, Sana. Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences. ESAIM: Probability and Statistics, Tome 9 (2005), pp. 38-73. doi : 10.1051/ps:2005003. http://www.numdam.org/articles/10.1051/ps:2005003/
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