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A stationary pairwise independent absolutely regular sequence for which the central limit theorem fails. (English) Zbl 0649.60017
A strictly stationary finite-state non-degenerate random sequence is constructed which satisfies pairwise independence and absolute regularity but fails to satisfy a central limit theorem. The mixing rate for absolute regularity is only slightly slower than that in a corresponding central limit theorem of Ibragimov.
Reviewer: R.C.Bradley

MSC:
60F05 Central limit and other weak theorems
60G10 Stationary stochastic processes
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