# Upcrossing inequalities for stationary sequences and applications

@inproceedings{Hochman2009UpcrossingIF, title={Upcrossing inequalities for stationary sequences and applications}, author={Michael Hochman}, year={2009} }

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.

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