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

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 tr...

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Bibliographic Details
Published in:Problems of information transmission 2017-04, Vol.53 (2), p.103-113
Main Author: Gurevich, B. M.
Format: Article
Language:English
Subjects:
Communications Engineering
Control
Electrical Engineering
Engineering
Heat of transformation
Information Storage and Retrieval
Information Theory
Markov processes
Networks
Random processes
Systems Theory
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Summary: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.
ISSN:0032-9460
1608-3253
DOI:10.1134/S0032946017020016