A counter example to central limit theorem in Hilbert spaces under a strong mixing condition

Abstract

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.

12 pages, Electronic Communications in Probability, Volume 19, 2014

References in corpus (2)

• A strictly stationary $\beta$-mixing process satisfying the central limit theorem but not the weak invariance principle
• Central limit theorems for Hilbert-space valued random fields satisfying a strong mixing condition