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2012 Uncomputably Noisy Ergodic Limits
Jeremy Avigad
Notre Dame J. Formal Logic 53(3): 347-350 (2012). DOI: 10.1215/00294527-1716757

Abstract

V’yugin has shown that there are a computable shift-invariant measure on 2N and a simple function f such that there is no computable bound on the rate of convergence of the ergodic averages Anf. Here it is shown that in fact one can construct an example with the property that there is no computable bound on the complexity of the limit; that is, there is no computable bound on how complex a simple function needs to be to approximate the limit to within a given ε.

Citation

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Jeremy Avigad. "Uncomputably Noisy Ergodic Limits." Notre Dame J. Formal Logic 53 (3) 347 - 350, 2012. https://doi.org/10.1215/00294527-1716757

Information

Published: 2012
First available in Project Euclid: 25 September 2012

zbMATH: 1258.03084
MathSciNet: MR2981012
Digital Object Identifier: 10.1215/00294527-1716757

Subjects:
Primary: 03F60
Secondary: 37A25

Rights: Copyright © 2012 University of Notre Dame

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Vol.53 • No. 3 • 2012
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