Different Closed-Form Expressions for Generalized Entropy Rates of Markov Chains

Valérie Girardin (), Loick Lhote () and Philippe Regnault ()
Additional contact information
Valérie Girardin: Université de Caen Normandie
Loick Lhote: Université de Caen Normandie
Philippe Regnault: Université de Reims Champagne-Ardenne

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 4, 1431-1452

Abstract: Abstract Closed-form expressions for generalized entropy rates of Markov chains are obtained through pertinent averaging. First, the rates are expressed in terms of Perron-Frobenius eigenvalues of perturbations of the transition matrices. This leads to a classification of generalized entropy functionals into five exclusive types. Then, a weighted expression is obtained in which the associated Perron-Frobenius eigenvectors play the same role as the stationary distribution in the well-known weighted expression of Shannon entropy rate. Finally, all terms are shown to bear a meaning in terms of dynamics of an auxiliary absorbing Markov chain through the notion of quasi-limit distribution. Illustration of important properties of the involved spectral elements is provided through application to binary Markov chains.

Keywords: Entropy rate; Ergodic Markov chain; Entropy distribution; Quasi-limit distribution; 94A17; 60J10; 15B48; 47B65 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-018-9679-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:21:y:2019:i:4:d:10.1007_s11009-018-9679-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-018-9679-3

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().