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

Large deviations and rates of convergence in the Birkhoff ergodic theorem: From Hölder continuity to continuity Full article

Journal

Doklady Mathematics
ISSN: 1064-5624 , E-ISSN: 1531-8362

Output data

Year: 2016, Volume: 93, Number: 1, Pages: 6-8 Pages count : 3 DOI: 10.1134/s106456241601004x

Authors

Kachurovskii A.G. ^1,2 , Podvigin I.V. ^1,2

Affiliations

1	Sobolev Institute of Mathematics
2	Novosibirsk State University

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.

Kachurovskii A.G. , Podvigin I.V.
Large deviations and rates of convergence in the Birkhoff ergodic theorem: From Hölder continuity to continuity
Doklady Mathematics. 2016. V.93. N1. P.6-8. DOI: 10.1134/s106456241601004x WOS Scopus РИНЦ OpenAlex

Качуровский A.Г. , Подвигин И.В.
Большие уклонения и скорости сходимости в эргодической теореме Биркгофа: переход от гёльдеровости к непрерывности
Доклады академии наук. 2016. Т.466. №1. С.12-15. DOI: 10.7868/s0869565216010060 РИНЦ OpenAlex

Web of science:	WOS:000373359900002
Scopus:	2-s2.0-84962145247
Elibrary:	27145562
OpenAlex:	W2321831239

DB	Citing
Web of science	5
Scopus	5
Elibrary	4
OpenAlex	5