## Electronic Communications in Probability

### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 62, 12 pp.

Dates
Accepted: 29 August 2014
First available in Project Euclid: 7 June 2016

https://projecteuclid.org/euclid.ecp/1465316764

Digital Object Identifier
doi:10.1214/ECP.v19-3249

Mathematical Reviews number (MathSciNet)
MR3254741

Zentralblatt MATH identifier
1334.60020

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G10: Stationary processes

Rights

#### Citation

Giraudo, Davide; Volny, Dalibor. A counter example to central limit theorem in Hilbert spaces under a strong mixing condition. Electron. Commun. Probab. 19 (2014), paper no. 62, 12 pp. doi:10.1214/ECP.v19-3249. https://projecteuclid.org/euclid.ecp/1465316764

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