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 Sibirsk. Mat. Zh., 2012, Volume 53, Number 5, Pages 1102–1110 (Mi smj2333)

Constants in the estimates of the convergence rate in the Birkhoff ergodic theorem with continuous time

V. V. Sedalishchev

Novosibirsk State University, Novosibirsk

Abstract: For the case of continuous time, we prove inequalities that make it possible, in the presence of power-type estimates of the convergence rate in the von Neumann ergodic theorem, to obtain estimates for the convergence rate in the Birkhoff ergodic theorem. These results have obvious exact analogs in the class of wide-sense stationary stochastic processes.

Keywords: von Neumann's ergodic theorem, Birkhoff's ergodic theorem, convergence rate of ergodic averages, spectral measure, correlation function, wide-sense stationary stochastic process.

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English version:
Siberian Mathematical Journal, 2012, 53:5, 882–888

Bibliographic databases:

UDC: 517.987+519.214

Citation: V. V. Sedalishchev, “Constants in the estimates of the convergence rate in the Birkhoff ergodic theorem with continuous time”, Sibirsk. Mat. Zh., 53:5 (2012), 1102–1110; Siberian Math. J., 53:5 (2012), 882–888

Citation in format AMSBIB
\Bibitem{Sed12} \by V.~V.~Sedalishchev \paper Constants in the estimates of the convergence rate in the Birkhoff ergodic theorem with continuous time \jour Sibirsk. Mat. Zh. \yr 2012 \vol 53 \issue 5 \pages 1102--1110 \mathnet{http://mi.mathnet.ru/smj2333} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3057930} \transl \jour Siberian Math. J. \yr 2012 \vol 53 \issue 5 \pages 882--888 \crossref{https://doi.org/10.1134/S0037446612050138} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000310374900013} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84868123243} 

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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. 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
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