This article is cited in 10 papers

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

A. G. Kachurovskii^a, V. V. Sedalishchev<sup>b

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University

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.

UDC: 517.987+519.214

Received: 19.08.2009

DOI: 10.4213/mzm8718

 English version: Mathematical Notes, 2010, 87:5, 720–727

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