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Probl. Peredachi Inf., 2017, Volume 53, Issue 2, Pages 3–15 (Mi ppi2232)  

Information Theory

Entropy of a stationary process and entropy of a shift transformation in its sample space

B. M. Gurevichab

a Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
b Lomonosov Moscow State University, Moscow, Russia

Abstract: We construct a class of non-Markov discrete-time stationary random processes with countably many states for which the entropy of the one-dimensional distribution is infinite, while the conditional entropy of the “present” given the “past” is finite and coincides with the metric entropy of a shift transformation in the sample space. Previously, such situation was observed in the case of Markov processes only.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00379
Supported in part by the Russian Foundation for Basic Research, project no. 14-01-00379.


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English version:
Problems of Information Transmission, 2017, 53:2, 103–113

Bibliographic databases:

UDC: 621.391.1+519.2
Received: 16.06.2016
Revised: 06.11.2016

Citation: B. M. Gurevich, “Entropy of a stationary process and entropy of a shift transformation in its sample space”, Probl. Peredachi Inf., 53:2 (2017), 3–15; Problems Inform. Transmission, 53:2 (2017), 103–113

Citation in format AMSBIB
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\paper Entropy of a~stationary process and entropy of a~shift transformation in its sample space
\jour Probl. Peredachi Inf.
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\vol 53
\issue 2
\pages 3--15
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\jour Problems Inform. Transmission
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\vol 53
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\pages 103--113
\crossref{https://doi.org/10.1134/S0032946017020016}
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