Electronic Communications in Probability

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

Davide Giraudo and Dalibor Volny

Full-text: Open access

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

Permanent link to this document
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

Keywords
Central limit theorem Hilbert space mixing conditions strictly stationary process

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

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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