Email this article Large deviations and rates of convergence in the Birkhoff ergodic theorem: From Hölder continuity to continuity
- Authors: Kachurovskii A.G.1,2, Podvigin I.V.1,2
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Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch
- Novosibirsk State University
- Issue: Vol 93, No 1 (2016)
- Pages: 6-8
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223343
- DOI: https://doi.org/10.1134/S106456241601004X
- ID: 223343
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Abstract
It is established that, for ergodic dynamical systems, upper estimates for the decay of large deviations of ergodic averages for (non-Hölder) continuous almost everywhere averaged functions have the same asymptotics as in the Hölder continuous case. The results are applied to obtaining the corresponding estimates for large deviations and rates of convergence in the Birkhoff ergodic theorem with non-Hölder averaged functions in certain popular chaotic billiards, such as the Bunimovich stadiums and the planar periodic Lorentz gas.
About the authors
A. G. Kachurovskii
Sobolev Institute of Mathematics, Siberian Branch; Novosibirsk State University
Email: ipodvigin@math.nsc.ru
Russian Federation, pr. Akademika Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
I. V. Podvigin
Sobolev Institute of Mathematics, Siberian Branch; Novosibirsk State University
Author for correspondence.
Email: ipodvigin@math.nsc.ru
Russian Federation, pr. Akademika Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
