Fluctuations of ergodic averages
Kalikow, Steven ; Weiss, Benjamin
Illinois J. Math., Tome 43 (1999) no. 3, p. 480-488 / Harvested from Project Euclid
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We discuss universal estimates for the probability that there are many fluctuations in the ergodic averages of $L^{1}$ functions. Our methods involve an effective Vitali covering type of theorem and are valid for $\mathbb{Z}^{d}$ actions, for any $d \in \mathbb{N}$. For nonnegative functions we get an exponential decay for the probability of a large number of fluctuations.
Publié le : 1999-09-15
Classification:  28D05 
@article{1255985104,
     author = {Kalikow, Steven and Weiss, Benjamin},
     title = {Fluctuations of ergodic averages},
     journal = {Illinois J. Math.},
     volume = {43},
     number = {3},
     year = {1999},
     pages = { 480-488},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255985104}
}

Kalikow, Steven; Weiss, Benjamin. Fluctuations of ergodic averages. Illinois J. Math., Tome 43 (1999) no. 3, pp.  480-488. http://gdmltest.u-ga.fr/item/1255985104/