Statistical Estimation of Measure Invariants
نویسنده
چکیده
New invariants of measures, called the β-statentropy, are described. They are similar to the entropy and the HP -spectrum for dimensions. The βstatentropy admits construction of a statistical estimator calculated by n independent points distributed in accordance with a given measure. The accuracy of this estimator is O(n−c), where c is some constant, and the complexity of calculation is O(n2). It is shown that for an exact dimensional measure the 0-statentropy coincides with the Hausdorff dimension, and for a Markov measure the β-statentropy coincides with the HP -spectrum for dimensions. An application of the β-statentropy to finding the entropy and dimensional characteristics of dynamical systems is described.
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