# Upcrossing inequalities for stationary sequences and applications

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 Kingmans subadditive ergodic theorem, the Shannon-MacMillan-Breiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.

Author: Michael Hochman

Source: https://archive.org/