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Matematicheskie Zametki, 2010, Volume 87, Issue 5, Pages 756–763
DOI: https://doi.org/10.4213/mzm8718 (Mi mzm8718) 		 
This article is cited in 9 scientific papers (total in 9 papers)

On the Constants in the Estimates of the Rate of Convergence in von Neumann's Ergodic Theorem

A. G. Kachurovskiia, V. V. Sedalishchevb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University
Full-text PDF (410 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm8718
Abstract: We study the rate of convergence in von Neumann's ergodic theorem. We obtain constants connecting the power rate of convergence of ergodic means and the power singularity at zero of the spectral measure of the corresponding dynamical system (these concepts are equivalent to each other). All the results of the paper have obvious exact analogs for wide-sense stationary stochastic processes.
Keywords: von Neumann's ergodic theorem, ergodic mean, spectral measure, dynamical system, wide-sense stationary stochastic process, correlation coefficient, Darboux sum.
Received: 19.08.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 5, Pages 720–727
DOI: https://doi.org/10.1134/S000143461005010X
Bibliographic databases:
Document Type: Article
UDC: 517.987+519.214
Language: Russian
Citation: A. G. Kachurovskii, V. V. Sedalishchev, “On the Constants in the Estimates of the Rate of Convergence in von Neumann's Ergodic Theorem”, Mat. Zametki, 87:5 (2010), 756–763; Math. Notes, 87:5 (2010), 720–727
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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