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On the Entropy for Semi-Markov Processes

Valerie Girardin and Nikolaos Limnios
Journal of Applied Probability
Vol. 40, No. 4 (Dec., 2003), pp. 1060-1068
Stable URL: http://www.jstor.org/stable/3216060
Page Count: 9
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On the Entropy for Semi-Markov Processes
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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.

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