# Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences

Jérôme Dedecker; Sana Louhichi

ESAIM: Probability and Statistics (2010)

- Volume: 9, page 38-73
- ISSN: 1292-8100

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topDedecker, Jérôme, and Louhichi, Sana. "Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences." ESAIM: Probability and Statistics 9 (2010): 38-73. <http://eudml.org/doc/104341>.

@article{Dedecker2010,

abstract = {
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.
},

author = {Dedecker, Jérôme, Louhichi, Sana},

journal = {ESAIM: Probability and Statistics},

keywords = {Infinitely
divisible distributions; Lévy processes; weak dependence;
association; binary random variables; number of exceedances.; Infinitely divisible distributions; association; number of exceedances},

language = {eng},

month = {3},

pages = {38-73},

publisher = {EDP Sciences},

title = {Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences},

url = {http://eudml.org/doc/104341},

volume = {9},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 9

SP - 38

EP - 73

AB -
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.

LA - eng

KW - Infinitely
divisible distributions; Lévy processes; weak dependence;
association; binary random variables; number of exceedances.; Infinitely divisible distributions; association; number of exceedances

UR - http://eudml.org/doc/104341

ER -

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