# zbMATH — the first resource for mathematics

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
Full Text: