Local information geometry for statistical analysis of high-order binary Markov chains

Authors

  • Valeriy A. Voloshko Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus , Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

Keywords:

information geometry, tangent space, asymptotic distribution, binary sequence, Markov manifold

Abstract

At the 14th International conference «Computer data analysis and modelling: stochastics and data analysis» the author presented some new results on asymptotic properties of statistics derived from purely random (uniformly distributed) binary sequence of increasing length. These results are obtained by methods of information geometry applied to manifolds of Markov probability distributions on the set of infinite binary sequences. In this paper the underlying information-geometric theory and the technics of proofs are describe in more detail. By few examples, it is shown how finding probabilistic and statistical properties comes down to geometric and combinatorial computations.

Author Biography

  • Valeriy A. Voloshko, Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus, Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics); accosiate professor at the department of mathematical modelling and data analysis, faculty of applied mathematics and computer science, Belarusian State University, and head of the sector of computer data analysis, Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University

References

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Published

2026-06-04

Issue

No. 1 (2026): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics

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How to Cite

[1]
Voloshko, V.A. 2026. Local information geometry for statistical analysis of high-order binary Markov chains. Journal of the Belarusian State University. Mathematics and Informatics. 1 (Jun. 2026), 61–74.