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Matematicheskie Zametki, 2005, Volume 77, Issue 6, Pages 903–916
DOI: https://doi.org/10.4213/mzm2546 (Mi mzm2546) 		 
This article is cited in 7 scientific papers (total in 7 papers)

A Consistent Estimator of the Entropy of Measures and Dynamical Systems

E. A. Timofeev

P. G. Demidov Yaroslavl State University
Full-text PDF (232 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm2546
Abstract: In the paper, a new invariant of measures and dynamical systems, called statentropy, is described. A statistical estimator for statentropy, computed without using auxiliary estimates of measures, is constructed. It is proved that the proposed statistical estimator is consistent under fairly general restrictions. We show that for exact dimensional measures, statentropy coincides with the Hausdorff dimension of the measure, and for ergodic dynamical systems, it coincides with the metric entropy of the map.
Received: 24.12.2002
Revised: 25.10.2004
English version:
Mathematical Notes, 2005, Volume 77, Issue 6, Pages 831–842
DOI: https://doi.org/10.1007/s11006-005-0083-2
Bibliographic databases:
UDC: 519.987
Language: Russian
Citation: E. A. Timofeev, “A Consistent Estimator of the Entropy of Measures and Dynamical Systems”, Mat. Zametki, 77:6 (2005), 903–916; Math. Notes, 77:6 (2005), 831–842
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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