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June 2006 Entropy for semi-Markov processes with Borel state spaces: asymptotic equirepartition properties and invariance principles
Valerie Girardin, Nikolaos Limnios
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Bernoulli 12(3): 515-533 (June 2006). DOI: 10.3150/bj/1151525134

Abstract

The aim of this paper is to define the entropy rate of a semi-Markov process with a Borel state space by extending the strong asymptotic equirepartition property (also called the ergodic theorem of information theory or Shannon-McMillan-Breiman theorem) to this class of non-stationary processes. The mean asymptotic equirepartition property (also called the Shannon-McMillan theorem) is also proven to hold. The relative entropy rate between two semi-Markov processes is defined. All earlier results concerning entropy for semi-Markov processes, jump Markov processes and Markov chains thus appear as special cases. Two invariance principles are established for entropy, one for the central limit theorem and the other for the law of the iterated logarithm.

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Valerie Girardin. Nikolaos Limnios. "Entropy for semi-Markov processes with Borel state spaces: asymptotic equirepartition properties and invariance principles." Bernoulli 12 (3) 515 - 533, June 2006. https://doi.org/10.3150/bj/1151525134

Information

Published: June 2006
First available in Project Euclid: 28 June 2006

zbMATH: 1114.60070
MathSciNet: MR2232730
Digital Object Identifier: 10.3150/bj/1151525134

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

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Vol.12 • No. 3 • June 2006
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