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

Abstract

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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.

How to cite

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Dedecker, 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 -

References

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