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

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 transformation in the sample space. Previously, such situation was observed in the case of Markov processes only. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

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

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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946017020016
Publisher site
See Article on Publisher Site

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.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 13, 2017

References

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