This article is cited in 5 papers

Constants in the estimates of the convergence rate in the Birkhoff ergodic theorem with continuous time

V. V. Sedalishchev

Novosibirsk State University, Novosibirsk

Abstract: For the case of continuous time, we prove inequalities that make it possible, in the presence of power-type estimates of the convergence rate in the von Neumann ergodic theorem, to obtain estimates for the convergence rate in the Birkhoff ergodic theorem. These results have obvious exact analogs in the class of wide-sense stationary stochastic processes.

Keywords: von Neumann's ergodic theorem, Birkhoff's ergodic theorem, convergence rate of ergodic averages, spectral measure, correlation function, wide-sense stationary stochastic process.

UDC: 517.987+519.214

Received: 30.12.2011

 English version: Siberian Mathematical Journal, 2012, 53:5, 882–888

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