Different Closed-Form Expressions for Generalized Entropy Rates of Markov Chains - École Nationale Supérieure d’Ingénieurs de Caen Accéder directement au contenu
Article Dans Une Revue Methodology and Computing in Applied Probability Année : 2018

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

Loïck Lhote
Philippe Regnault
  • Fonction : Auteur
  • PersonId : 961830

Résumé

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.
Fichier principal
Vignette du fichier
Entropy_rates_Markov_Chains_preprint_hal.pdf (233.66 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01966810 , version 1 (29-12-2018)

Identifiants

Citer

Valerie Girardin, Loïck Lhote, Philippe Regnault. Different Closed-Form Expressions for Generalized Entropy Rates of Markov Chains. Methodology and Computing in Applied Probability, 2018, ⟨10.1007/s11009-018-9679-3⟩. ⟨hal-01966810⟩
98 Consultations
329 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More