Measuring the Rate of Convergence in the Birkhoff Ergodic Theorem

A. G. Kachurovskii; I. V. Podvigin

doi:10.1134/S0001434619070058

Measuring the Rate of Convergence in the Birkhoff Ergodic Theorem

A. G. Kachurovskii, I. V. Podvigin

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Estimates of the rate of convergence in the Birkhoff ergodic theorem which hold almost everywhere are considered. For the action of an ergodic automorphism, the existence of such estimates is proved, their structure is studied, and unimprovability questions are considered.

Original language	English
Pages (from-to)	52-62
Number of pages	11
Journal	Mathematical Notes
Volume	106
Issue number	1-2
DOIs	https://doi.org/10.1134/S0001434619070058
Publication status	Published - 1 Jul 2019

Keywords

individual ergodic theorem
lattice
rate of convergence in ergodic theorems
return time
unimprovability of estimates

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10.1134/S0001434619070058

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title = "Measuring the Rate of Convergence in the Birkhoff Ergodic Theorem",

abstract = "Estimates of the rate of convergence in the Birkhoff ergodic theorem which hold almost everywhere are considered. For the action of an ergodic automorphism, the existence of such estimates is proved, their structure is studied, and unimprovability questions are considered.",

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AU - Kachurovskii, A. G.

AU - Podvigin, I. V.

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N2 - Estimates of the rate of convergence in the Birkhoff ergodic theorem which hold almost everywhere are considered. For the action of an ergodic automorphism, the existence of such estimates is proved, their structure is studied, and unimprovability questions are considered.

AB - Estimates of the rate of convergence in the Birkhoff ergodic theorem which hold almost everywhere are considered. For the action of an ergodic automorphism, the existence of such estimates is proved, their structure is studied, and unimprovability questions are considered.

KW - individual ergodic theorem

KW - lattice

KW - rate of convergence in ergodic theorems

KW - return time

KW - unimprovability of estimates

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Measuring the Rate of Convergence in the Birkhoff Ergodic Theorem

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Keywords

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