Upcrossing inequalities for stationary sequences and applications

Hochman, Michael

Ann. Probab., Tome 37 (2009) no. 1, p. 2135-2149 / Harvested from Project Euclid

Résumé

For arrays (S_i,j)_1≤i≤j of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process (S_1,n)_n=1^∞ can be bounded in terms of a measure of the “mean subadditivity” of the process (S_i,j)_1≤i≤j. We derive universal upcrossing inequalities with exponential decay for Kingman’s subadditive ergodic theorem, the Shannon–MacMillan–Breiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.

Publié le : 2009-11-15
Classification: Ergodic theorem, Shannon–McMillan–Breiman theorem, upcrossing inequalities entropy, Kolmogorov complexity, almost everywhere convergence, 37A30, 37A35, 60G10, 60G17, 94A17, 68Q30

@article{1258380784,
     author = {Hochman, Michael},
     title = {Upcrossing inequalities for stationary sequences and applications},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 2135-2149},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258380784}
}

Hochman, Michael. Upcrossing inequalities for stationary sequences and applications. Ann. Probab., Tome 37 (2009) no. 1, pp.  2135-2149. http://gdmltest.u-ga.fr/item/1258380784/