Large deviations and rates of convergence in the Birkhoff ergodic theorem: from Hölder continuity to continuity

DOI10.1134/S106456241601004XzbMath1362.37014MaRDI QIDQ294308

A. G. Kachurovskii, I. V. Podvigin

Publication date: 16 June 2016

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

large deviationschaotic billiardsergodic dynamical systems

Mathematics Subject Classification ID

Large deviations (60F10) Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Dynamical aspects of statistical mechanics (37A60)

Related Items (6)

Estimates for Correlation in Dynamical Systems: From Hölder Continuous Functions to General Observables ⋮ On the rate of convergence in the individual ergodic theorem for the action of a semigroup ⋮ Large deviations of Birkhoff's sums via the approximation of observables ⋮ Large Deviations of the Ergodic Averages: From Hölder Continuity to Continuity Almost Everywhere ⋮ A uniform estimate for rate functions in large deviations ⋮ Concentration inequalities and rates of convergence of the ergodic theorem for countable shifts with Gibbs measures

Cites Work

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• Rates of convergence in ergodic theorems for certain billiards and Anosov diffeomorphisms
• Rate of convergence in ergodic theorems for the planar periodic Lorentz gas
• Correlations, large deviations, and rates of convergence in ergodic theorems for characteristic functions
• From rates of mixing to recurrence times via large deviations
• Improved estimates for correlations in billiards
• Large deviations and the rate of convergence in the Birkhoff ergodic theorem
• Large and moderate deviations for slowly mixing dynamical systems
• Large deviations in non-uniformly hyperbolic dynamical systems

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