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Convergence to infinitely divisible distributions with finite variance for someweakly dependent sequences
Jérôme Dedecker, Sana Louhichi
Journal:

ESAIM: Probability and Statistics / Volume 9 / February 2005

Published online by Cambridge University Press:

15 November 2005, pp. 38-73

Print publication:

February 2005
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We continue the investigation started in a previous paper, onweak convergence to infinitely divisible distributions with finitevariance. In the present paper, we study this problem for someweakly dependent random variables, including in particularassociated sequences. We obtain minimal conditions expressed interms of individual random variables. As in the i.i.d. case, wedescribe the convergence to the Gaussian and the purelynon-Gaussian parts of the infinitely divisible limit. We alsodiscuss the rate of Poisson convergence and emphasize the specialcase of Bernoulli random variables. The proofs aremainly based on Lindeberg's method.