St. Petersburg Mathematical Society

Author(s): E. A. Timofeev
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 17 (2005), vypusk 3.
Journal: St. Petersburg Math. J. 17 (2006), 527-551.
MSC (2000): Primary 28A75, 62L20
Posted: March 21, 2006
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Abstract: New invariants of measures, called the $\beta$ -statentropy, are described. They are similar to the entropy and the

-spectrum for dimensions. The $\beta$ -statentropy admits construction of a statistical estimator calculated by

independent points distributed in accordance with a given measure. The accuracy of this estimator is $\mathcal{O}(n^{-c})$ , where

is some constant, and the complexity of calculation is $\mathcal{O}(n^2)$ .

It is shown that for an exact dimensional measure the 0-statentropy coincides with the Hausdorff dimension, and for a Markov measure the $\beta$ -statentropy coincides with the

-spectrum for dimensions.

An application of the $\beta$ -statentropy to finding the entropy and dimensional characteristics of dynamical systems is described.

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Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 28A75, 62L20

E. A. Timofeev
Affiliation: Yaroslavl{'} State University, Sovetskaya Street 14, Yaroslavl{'} 150000, Russia
Email: tim@uniyar.ac.ru

DOI: 10.1090/S1061-0022-06-00919-8
PII: S 1061-0022(06)00919-8
Keywords: $\beta$-statentropy, statistical estimator, exact dimensional measure, Markov measure
Received by editor(s): 20/FEB/2004
Posted: March 21, 2006
Copyright of article: Copyright 2006, American Mathematical Society

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ISSN: 1547-7371(e) ISSN: 1061-0022(p)

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