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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 5, Pages 1102–1110
(Mi smj2333)
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This article is cited in 6 scientific papers (total in 6 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.
Received: 30.12.2011
Citation:
V. V. Sedalishchev, “Constants in the estimates of the convergence rate in the Birkhoff ergodic theorem with continuous time”, Sibirsk. Mat. Zh., 53:5 (2012), 1102–1110; Siberian Math. J., 53:5 (2012), 882–888
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https://www.mathnet.ru/eng/smj2333 https://www.mathnet.ru/eng/smj/v53/i5/p1102
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Abstract page: | 541 | Full-text PDF : | 156 | References: | 73 | First page: | 7 |
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