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Central limit theorem by moments. (English) Zbl 1133.60311
Summary: In a previous central limit theorem for moments, it has been proved that the moments converge to those of the normal distribution if the moments of the sums are asymptotically independent [cf. R. Blacher, C. R. Acad. Sci., Paris, Sér. I 311, 465–468 (1990; Zbl 0706.60025)]. In this paper we generalize this result by adding a negligible sequence to these sums. So, we can prove that the moments of some functionals of strong mixing sequences converge.

MSC:
60F05 Central limit and other weak theorems
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