Upcrossing inequalities for stationary sequences and applications

Michael Hochman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


For arrays (Si,j)1≤i≤j of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process (S1,n)n=1 can be bounded in terms of a measure of the "mean subadditivity" of the process (Si,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.

Original languageAmerican English
Pages (from-to)2135-2149
Number of pages15
JournalAnnals of Probability
Issue number6
StatePublished - Nov 2009


  • Almost everywhere convergence
  • Ergodic theorem
  • Kolmogorov complexity
  • Shannon-McMillan-Breiman theorem
  • Upcrossing inequalities entropy


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