On the entropy for semi-Markov processes
Valerie Girardin and Nikolaos Limnios
Source: J. Appl. Probab.
Volume 40, Number 4
(2003), 1060-1068.
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.
Primary Subjects: 60K15, 60J25, 62B10, 94A17
Keywords: Relative entropy; entropy rate; semi-Markov process; pure jump Markov process
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1067436100
Digital Object Identifier: doi:10.1239/jap/1067436100
Mathematical Reviews number (MathSciNet):
MR2012686
Zentralblatt MATH identifier:
02103422
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