A counter example to central limit theorem in Hilbert spaces under a strong mixing condition
Probability
2015-03-31 v2
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.
Keywords
Cite
@article{arxiv.1401.1936,
title = {A counter example to central limit theorem in Hilbert spaces under a strong mixing condition},
author = {Davide Giraudo and Dalibor Volný},
journal= {arXiv preprint arXiv:1401.1936},
year = {2015}
}
Comments
12 pages, Electronic Communications in Probability, Volume 19, 2014