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