Upcrossing inequalities for stationary sequences and applications

DOI10.1214/09-AOP460zbMath1196.37014arXivmath/0608311OpenAlexW2076112250MaRDI QIDQ971935

Michael Hochman

Publication date: 17 May 2010

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608311

zbMATH Keywords

ergodic theoremsupcrossing inequalitiesmean subadditivitystationary random variables

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Algorithmic information theory (Kolmogorov complexity, etc.) (68Q30) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Sample path properties (60G17) Ergodic theorems, spectral theory, Markov operators (37A30) Measures of information, entropy (94A17)

Related Items (11)

On stability of probability laws with respect to small violations of algorithmic randomness ⋮ UNIVERSAL CODING AND PREDICTION ON ERGODIC RANDOM POINTS ⋮ Quasiperiodicity and Non-computability in Tilings ⋮ Ergodic theorems and converses for PSPACE functions ⋮ The metamathematics of ergodic theory ⋮ Randomness and initial segment complexity for measures ⋮ Local stability of ergodic averages ⋮ Martin-Löf random quantum states ⋮ Martin-Löf randomness implies multiple recurrence in effectively closed sets ⋮ Oscillation and the mean ergodic theorem for uniformly convex Banach spaces ⋮ Computable Measure Theory and Algorithmic Randomness

Cites Work

• Kolmogorov's contributions to information theory and algorithmic complexity
• Fluctuations of ergodic averages
• Oscillations of means in the ergodic theorem
• An upcrossing inequality with applications
• On upcrossing inequalities for subadditive superstationary processes
• Oscillation in ergodic theory
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