English

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