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Convergence to infinitely divisible distributions with finite variance for someweakly dependent sequences
Published online by Cambridge University Press: 15 November 2005
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.
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- Research Article
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- © EDP Sciences, SMAI, 2005
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