Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences
ESAIM: Probability and Statistics, Tome 9 (2005), pp. 38-73.

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.

DOI : https://doi.org/10.1051/ps:2005003
Classification : 60E07,  60F05
Mots clés : infinitely divisible distributions, Lévy processes, weak dependence, association, binary random variables, number of exceedances
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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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