On standard normal convergence of the multivariate Student -statistic for symmetric random vectors.

Giné, Evarist; Götze, Friedrich

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

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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....