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On the entropy for semi-Markov processes

Published online by Cambridge University Press:  14 July 2016

Valerie Girardin*
Affiliation:
Université de Caen
Nikolaos Limnios*
Affiliation:
Université de Technologie de Compiègne
*
Postal address: Mathématiques, Campus II, Université de Caen, BP 5186, 14032 Caen, France. Email address: girardin@math.unicaen.fr
∗∗Postal address: Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, BP 20529, 60205 Compiègne Cedex, France.

Abstract

The aim of this paper is to define the entropy of a finite semi-Markov process. We define the entropy of the finite distributions of the process, and obtain explicitly its entropy rate by extending the Shannon–McMillan–Breiman theorem to this class of nonstationary continuous-time processes. The particular cases of pure jump Markov processes and renewal processes are considered. The relative entropy rate between two semi-Markov processes is also defined.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2003 

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