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Entropy 2014, 16(3), 1396-1413; doi:10.3390/e16031396

Infinite Excess Entropy Processes with Countable-State Generators

1
Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA
2
Mathematics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA
3
Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA
4
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Present Address: Mathematics Department, Technion—Israel Institute of Technology, Technion City, Haifa 3200003, Israel
*
Author to whom correspondence should be addressed.
Received: 20 December 2013 / Revised: 24 February 2014 / Accepted: 5 March 2014 / Published: 10 March 2014
(This article belongs to the Special Issue Information in Dynamical Systems and Complex Systems)
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Abstract

We present two examples of finite-alphabet, infinite excess entropy processes generated by stationary hidden Markov models (HMMs) with countable state sets. The first, simpler example is not ergodic, but the second is. These are the first explicit constructions of processes of this type. View Full-Text
Keywords: stationary stochastic process; hidden Markov model; epsilon-machine; ergodicity; entropy rate; excess entropy; mutual information stationary stochastic process; hidden Markov model; epsilon-machine; ergodicity; entropy rate; excess entropy; mutual information
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Travers, N.F.; Crutchfield, J.P. Infinite Excess Entropy Processes with Countable-State Generators. Entropy 2014, 16, 1396-1413.

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