Geodesic
Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems
Sbornik. Mathematics, Tome 202 (2011) no. 8, pp. 1105-1125

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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, wide-sense stationary processes.
Mots-clés : correlation coefficients 
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     title = {Constants in estimates for the rates of convergence in von {Neumann's} and {Birkhoff's} ergodic theorems},
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A. G. Kachurovskii; V. V. Sedalishchev. Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems. Sbornik. Mathematics, Tome 202 (2011) no. 8, pp. 1105-1125. http://geodesic.mathdoc.fr/item/SM_2011_202_8_a1/