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

DOI10.1214/ECP.V19-3249zbMATH Open1334.60020arXiv1401.1936OpenAlexW2028364581MaRDI QIDQ457821

Davide Giraudo, Dalibor Volný

Publication date: 29 September 2014

Published in: Electronic Communications in Probability (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1401.1936

zbMATH Keywords

Hilbert spacecentral limit theoremmixing conditionsstrictly stationary process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10)

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