平稳序列的上穿不等式及其应用
Upcrossing inequalities for stationary sequences and applications
摘要：
对于阵列$(S_{i,j})_{1\leq i\leq j}$的随机变量是平稳的，在适当的意义上，我们表明，过程$(S_{1,n})_{n=1}^{\infty}$的波动可以有界的“平均次加性”的过程$(S_{i,j})_{1\leq i\leq j}$的措施。本文对Kingman次可加性遍历定理、Shannon-MacMillan-Breiman定理和平稳样本的Kolmogorov复杂性的收敛性给出了指数衰减的普适上穿不等式.
英文摘要：
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 Shannon--MacMillan--Breiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.
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