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November 2009 Upcrossing inequalities for stationary sequences and applications
Michael Hochman
Ann. Probab. 37(6): 2135-2149 (November 2009). DOI: 10.1214/09-AOP460

Abstract

For arrays (Si,j)1≤ij 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≤ij. 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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Michael Hochman. "Upcrossing inequalities for stationary sequences and applications." Ann. Probab. 37 (6) 2135 - 2149, November 2009. https://doi.org/10.1214/09-AOP460

Information

Published: November 2009
First available in Project Euclid: 16 November 2009

zbMATH: 1196.37014
MathSciNet: MR2573553
Digital Object Identifier: 10.1214/09-AOP460

Subjects:
Primary: 37A30, 37A35, 60G10, 60G17, 68Q30, 94A17

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 6 • November 2009
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