Large deviations and the rate of convergence in the Birkhoff ergodic theorem

DOI10.1134/S0001434613090228zbMath1370.37012OpenAlexW2133747049MaRDI QIDQ2436386

A. G. Kachurovskii, I. V. Podvigin

Publication date: 24 February 2014

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434613090228

zbMATH Keywords

rates of convergencelarge deviationspointwise ergodic theoremAnosov system

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Nonstandard measure theory (28E05)

Related Items

Large deviations and rates of convergence in the Birkhoff ergodic theorem: from Hölder continuity to continuity, Lower bound for the supremum of ergodic averages for \(\mathbb{Z}^d\) and \(\mathbb{R}^d\)-actions, On the rate of convergence in the individual ergodic theorem for the action of a semigroup, Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems, Large Deviations of the Ergodic Averages: From Hölder Continuity to Continuity Almost Everywhere, Interrelation between the convergence rates in von Neumann's and Birkhoff's ergodic theorems, Correlations, large deviations, and rates of convergence in ergodic theorems for characteristic functions, Measuring the rate of convergence in the Birkhoff ergodic theorem, Zero-one law for the rates of convergence in the Birkhoff ergodic theorem with continuous time

Cites Work

• Unnamed Item
• Large deviation asymptotics for Anosov flows
• A large deviations bound for the Teichmüller flow on the moduli space of abelian differentials
• Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems
• Large deviations for nonuniformly hyperbolic systems
• Large and moderate deviations for slowly mixing dynamical systems
• The rate of convergence in ergodic theorems