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 Mat. Zametki, 2013, Volume 94, Issue 4, Pages 569–577 (Mi mz9352)

This article is cited in 7 scientific papers (total in 7 papers)

Large Deviations and the Rate of Convergence in the Birkhoff Ergodic Theorem

A. G. Kachurovskiia, I. V. Podviginb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: For bounded averaged functions, we prove the equivalence of the power-law and exponential rates of convergence in the Birkhoff individual ergodic theorem with the same asymptotics of the probability of large deviations in this theorem.

Keywords: pointwise ergodic theorem, rates of convergence in ergodic theorems, large deviations, billiards, Anosov systems.

DOI: https://doi.org/10.4213/mzm9352

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English version:
Mathematical Notes, 2013, 94:4, 524–531

Bibliographic databases:

UDC: 517.987+519.214
Received: 27.02.2012

Citation: A. G. Kachurovskii, I. V. Podvigin, “Large Deviations and the Rate of Convergence in the Birkhoff Ergodic Theorem”, Mat. Zametki, 94:4 (2013), 569–577; Math. Notes, 94:4 (2013), 524–531

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. V. Sedalishchev, “Interrelation between the convergence rates in von Neumann's and Birkhoff's ergodic theorems”, Siberian Math. J., 55:2 (2014), 336–348
2. I. V. Podvigin, “On the Exponential Rate of Convergence in the Birkhoff Ergodic Theorem”, Math. Notes, 95:4 (2014), 573–576
3. I. V. Podvigin, “On the rate of convergence in the individual ergodic theorem for the action of a semigroup”, Siberian Adv. Math., 26:2 (2016), 139–151
4. A. G. Kachurovskii, I. V. Podvigin, “Correlations, large deviations, and rates of convergence in ergodic theorems for characteristic functions”, Dokl. Math., 91:2 (2015), 204–207
5. A. G. Kachurovskii, I. V. Podvigin, “Large deviations and rates of convergence in the Birkhoff ergodic theorem: From Holder continuity to continuity”, Doklady Mathematics, 93:1 (2016), 6–8
6. A. G. Kachurovskii, I. V. Podvigin, “Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems”, Trans. Moscow Math. Soc., 77 (2016), 1–53
7. A. G. Kachurovskiǐ, I. V. Podvigin, “Large deviations of the ergodic averages: from Hölder continuity to continuity almost everywhere”, Siberian Adv. Math., 28:1 (2018), 23–38
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