Packing dimensions of basins generated by distributions on a finite alphabet

DOI: https://doi.org/10.33581/2520-6508-2021-2-6-16

Abstract

We consider a space of infinite signals composed of letters from a finite alphabet. Each signal generates a sequence of empirical measures on the alphabet and the limit set corresponding to this sequence. The space of signals is partitioned into narrow basins consisting of signals with identical limit sets for the sequence of empirical measures and for each narrow basin its packing dimension is computed. Furthermore, we compute packing dimensions for two other types of basins defined in terms of limit behaviour of the empirical measures.

Author Biographies

Victor I. Bakhtin, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

doctor of science (physics and mathematics), full professor; professor at the department of functional analysis and analytical economics, faculty of mechanics and mathematics

Bruno Sadok, John Paul II Catholic University of Lublin, 14 Racławickie Alley, Lublin 20-950, Poland

lecturer at the department of probability theory and statistics, faculty of natural sciences and health

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Published
2021-08-05
Keywords: packing dimension, empirical measure, basin of a probability measure
How to Cite
Bakhtin, V. I., & Sadok, B. (2021). Packing dimensions of basins generated by distributions on a finite alphabet. Journal of the Belarusian State University. Mathematics and Informatics, 2, 6-16. https://doi.org/10.33581/2520-6508-2021-2-6-16
Issue
No 2 (2021): Journal of the Belarusian State University. Mathematics and Informatics
Section
Real, Complex and Functional Analysis

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