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A counter example to central limit theorem in Hilbert spaces under a strong mixing condition. (English) Zbl 1334.60020
Summary: We show that in a separable infinite dimensional Hilbert space, uniform integrability of the square of the norm of normalized partial sums of a strictly stationary sequence, together with a strong mixing condition, does not guarantee the central limit theorem.

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