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

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

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

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Published
2018-05-05
Keywords: Kullback – Leibler information function, t-entropy
How to Cite
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, 59-67. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/886
Issue
No 1 (2018): Journal of the Belarusian State University. Mathematics and Informatics
Section
Probability Theory and Mathematical Statistics

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