Skip to Main content Skip to Navigation
Journal articles

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

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.
Complete list of metadatas

Cited literature [32 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01966810
Contributor : Philippe Regnault <>
Submitted on : Saturday, December 29, 2018 - 6:26:02 PM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM
Long-term archiving on: : Saturday, March 30, 2019 - 2:07:18 PM

File

Entropy_rates_Markov_Chains_pr...
Files produced by the author(s)

Identifiers

Citation

Valerie Girardin, Loïck Lhote, Philippe Regnault. Different Closed-Form Expressions for Generalized Entropy Rates of Markov Chains. Methodology and Computing in Applied Probability, Springer Verlag, inPress, ⟨10.1007/s11009-018-9679-3⟩. ⟨hal-01966810⟩

Share

Metrics

Record views

101

Files downloads

160