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

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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.

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References

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    B. M. Gurevich

  2. Lomonosov Moscow State University, Moscow, Russia

    B. M. Gurevich

Authors
  1. B. M. Gurevich
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Correspondence to B. M. Gurevich.

Additional information

Original Russian Text © B.M. Gurevich, 2017, published in Problemy Peredachi Informatsii, 2017, Vol. 53, No. 2, pp. 3–15.

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

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Gurevich, B.M. Entropy of a stationary process and entropy of a shift transformation in its sample space. Probl Inf Transm 53, 103–113 (2017). https://doi.org/10.1134/S0032946017020016

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  • DOI: https://doi.org/10.1134/S0032946017020016

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