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Problemy Peredachi Informatsii, 2017, Volume 53, Issue 2, Pages 3–15 (Mi ppi2232)  
This article is cited in 1 scientific paper (total in 1 paper)

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
Full-text PDF (201 kB) Citations (1)
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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.
Received: 16.06.2016
Revised: 06.11.2016
English version:
Problems of Information Transmission, 2017, Volume 53, Issue 2, Pages 103–113
DOI: https://doi.org/10.1134/S0032946017020016
Bibliographic databases:
Document Type: Article
UDC: 621.391.1+519.2
Language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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