Upcrossing inequalities for stationary sequences and applications
Abstract
For arrays $(S_{i,j})_{1\leq i\leq j}$ of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process $(S_{1,n})_{n=1}^{\infty}$ can be bounded in terms of a measure of the ``mean subadditivity'' of the process $(S_{i,j})_{1\leq i\leq j}$. We derive universal upcrossing inequalities with exponential decay for Kingman's subadditive ergodic theorem, the ShannonMacMillanBreiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2006
 arXiv:
 arXiv:math/0608311
 Bibcode:
 2006math......8311H
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Probability;
 37A30;
 37A35;
 60G10;
 60G17;
 94A17;
 68Q30 (Primary)
 EPrint:
 Published in at http://dx.doi.org/10.1214/09AOP460 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)