Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.
@article{bwmeta1.element.bwnjournal-article-cmv84i1p75bwm,
author = {Emmanuel Lesigne and Dalibor Voln\'y},
title = {Large deviations for generic stationary processes},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {75-82},
zbl = {0973.28014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv84i1p75bwm}
}
Lesigne, Emmanuel; Volný, Dalibor. Large deviations for generic stationary processes. Colloquium Mathematicae, Tome 84/85 (2000) pp. 75-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv84i1p75bwm/
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