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Sbornik: Mathematics, 2011, Volume 202, Issue 8, Pages 1105–1125
DOI: https://doi.org/10.1070/SM2011v202n08ABEH004180 (Mi sm7717) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems

A. G. Kachurovskiia, V. V. Sedalishchevb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University, Mechanics and Mathematics Department
English version PDF (476 kB) Citations (17)
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DOI: https://doi.org/10.1070/SM2011v202n08ABEH004180
Abstract: The paper investigates estimates which relate two equivalent phenomena: the power-type rate of convergence in von Neumann's ergodic theorem and the power-type singularity at zero (with the same exponent) exhibited by the spectral measure of the function being averaged with respect to the corresponding dynamical system. The same rate of convergence is also estimated in terms of the rate of decrease of the correlation coefficients. Also, constants are found in analogous estimates for the power-type convergence in Birkhoff's ergodic theorem. All the results have exact analogues for wide-sense stationary stochastic processes.
Bibliography: 15 titles.
Keywords: rates of convergence in ergodic theorems, spectral measures, correlation coefficients, wide-sense stationary processes.
Received: 20.03.2010 and 30.09.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 8, Pages 21–40
DOI: https://doi.org/10.4213/sm7717
Bibliographic databases:
Document Type: Article
UDC: 517.987+519.214
MSC: Primary 28D05, 37A30; Secondary 37A50, 47A35, 60G10
Language: English
Original paper language: Russian
Citation: A. G. Kachurovskii, V. V. Sedalishchev, “Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems”, Mat. Sb., 202:8 (2011), 21–40; Sb. Math., 202:8 (2011), 1105–1125
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
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    References:83
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