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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 5, Pages 991–1010
DOI: https://doi.org/10.33048/smzh.2024.65.516 (Mi smj7905) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On convergence rates in the Birkhoff Ergodic Theorem

I. V. Podvigin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.33048/smzh.2024.65.516
Abstract: Basing on two approaches, we survey the results about convergence rates in the Birkhoff Ergodic Theorem. The first approach concerns almost everywhere pointwise estimates of ergodic averages, whereas the second relies upon the estimates of the measures of maximal deviations.
Keywords: convergence rates in ergodic theorems, correlations, large deviations.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0004
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0004).
Received: 09.08.2024
Revised: 09.08.2024
Accepted: 20.08.2024
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 5, Pages 1170–1186
DOI: https://doi.org/10.1134/S0037446624050161
Document Type: Article
UDC: 517.987
MSC: 35R30
Language: Russian
Citation: I. V. Podvigin, “On convergence rates in the Birkhoff Ergodic Theorem”, Sibirsk. Mat. Zh., 65:5 (2024), 991–1010; Siberian Math. J., 65:5 (2024), 1170–1186
Citation in format AMSBIB
\Bibitem{Pod24}
\by I.~V.~Podvigin
\paper On~convergence rates in the Birkhoff Ergodic Theorem
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 5
\pages 991--1010
\mathnet{http://mi.mathnet.ru/smj7905}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 5
\pages 1170--1186
\crossref{https://doi.org/10.1134/S0037446624050161}
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    		Сибирский математический журнал Siberian Mathematical Journal
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