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2014 A counter example to central limit theorem in Hilbert spaces under a strong mixing condition
Davide Giraudo, Dalibor Volny
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Electron. Commun. Probab. 19: 1-12 (2014). DOI: 10.1214/ECP.v19-3249

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.

Citation

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Davide Giraudo. Dalibor Volny. "A counter example to central limit theorem in Hilbert spaces under a strong mixing condition." Electron. Commun. Probab. 19 1 - 12, 2014. https://doi.org/10.1214/ECP.v19-3249

Information

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

zbMATH: 1334.60020
MathSciNet: MR3254741
Digital Object Identifier: 10.1214/ECP.v19-3249

Subjects:
Primary: 60F05
Secondary: 60G10

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