Geodesic
On the Constants in the Estimates of the Rate of Convergence in von~Neumann's Ergodic Theorem
Matematičeskie zametki, Tome 87 (2010) no. 5, pp. 756-763

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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, Darboux sum.
Mots-clés : correlation coefficient 
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     author = {A. G. Kachurovskii and V. V. Sedalishchev},
     title = {On the {Constants} in the {Estimates} of the {Rate} of {Convergence} in {von~Neumann's} {Ergodic} {Theorem}},
     journal = {Matemati\v{c}eskie zametki},
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A. G. Kachurovskii; V. V. Sedalishchev. On the Constants in the Estimates of the Rate of Convergence in von~Neumann's Ergodic Theorem. Matematičeskie zametki, Tome 87 (2010) no. 5, pp. 756-763. http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a8/