Introduction of the Kullback – Leibler information function by means of partitions of the probability space

Authors

  • Edvard E. Sokal Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

Keywords:

Kullback – Leibler information function, t-entropy

Abstract

In the paper we study the equivalence problem of two definitions of the Kullback – Leibler information function. It is commonly defined by integration of the logarithm of the density of one probability measure with respect to another. On the other hand, recently a concept of t-entropy of a dynamical system (that is a generalization of the information function) is actively explored, and this concept is defined by means of measurable partitions of the phase space. In the paper we investigate in which situations the two definitions are equivalent and in which ones they are not. In particular, the equivalence holds if both measures are finite.

Author Biography

  • Edvard E. Sokal, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

    postgraduate student at the department of functional analysis and analytical economics, faculty of mechanics and mathematics

References

  1. Borovkov A. A. Matematicheskaya statistika: Otsenka parametrov. Proverka gipotez. M. : Nauka, 1984 (in Russ.).
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  3. Antonevich A. B., Bakhtin V. I., Lebedev A. V. On t-entropy and variational principle for the spectral radii of transfer and weighted shift operators. Ergod. Theory Dyn. Syst. 2011. Vol. 31, issue 4. P. 995–1042. DOI: 10.1017/S0143385710000210.
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  5. Bakhtin V. I. [Spectral potential, Kullback action, and large deviation principle for finitely-additive measures]. Proc. of the Inst. of Math. of the Natl. Acad. of Sci. of Belarus. 2015. Vol. 24, No. 1. P. 1–13 (in Russ.).
  6. Bakhtin V., Sokal E. The Kullback – Leibler Information Function For Infinite Measures. Entropy. 2016. Vol. 18, issue 12. DOI:10.3390/e18120448.

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Published

2018-05-05

Issue

No. 1 (2018): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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How to Cite

[1]
Sokal, E.E. 2018. Introduction of the Kullback – Leibler information function by means of partitions of the probability space. Journal of the Belarusian State University. Mathematics and Informatics. 1 (May 2018), 59–67.