Infinite Excess Entropy Processes with Countable-State Generators

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.

Bibliographic Details
Main Authors:	Nicholas F. Travers, James P. Crutchfield
Format:	Article
Language:	English
Published:	MDPI AG 2014-03-01
Series:	Entropy
Subjects:	stationary stochastic process hidden Markov model epsilon-machine ergodicity entropy rate excess entropy mutual information
Online Access:	http://www.mdpi.com/1099-4300/16/3/1396

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spelling	doaj-b1ee960a3c8d413fbacfc3d8d007fa502020-11-24T23:58:41ZengMDPI AGEntropy1099-43002014-03-011631396141310.3390/e16031396e16031396Infinite Excess Entropy Processes with Countable-State GeneratorsNicholas F. Travers0James P. Crutchfield1Complexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USAComplexity Sciences Center, University of California at Davis, One Shields Avenue, Davis, CA 95616, USAWe 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.http://www.mdpi.com/1099-4300/16/3/1396stationary stochastic processhidden Markov modelepsilon-machineergodicityentropy rateexcess entropymutual information
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Nicholas F. Travers James P. Crutchfield
spellingShingle	Nicholas F. Travers James P. Crutchfield Infinite Excess Entropy Processes with Countable-State Generators Entropy stationary stochastic process hidden Markov model epsilon-machine ergodicity entropy rate excess entropy mutual information
author_facet	Nicholas F. Travers James P. Crutchfield
author_sort	Nicholas F. Travers
title	Infinite Excess Entropy Processes with Countable-State Generators
title_short	Infinite Excess Entropy Processes with Countable-State Generators
title_full	Infinite Excess Entropy Processes with Countable-State Generators
title_fullStr	Infinite Excess Entropy Processes with Countable-State Generators
title_full_unstemmed	Infinite Excess Entropy Processes with Countable-State Generators
title_sort	infinite excess entropy processes with countable-state generators
publisher	MDPI AG
series	Entropy
issn	1099-4300
publishDate	2014-03-01
description	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.
topic	stationary stochastic process hidden Markov model epsilon-machine ergodicity entropy rate excess entropy mutual information
url	http://www.mdpi.com/1099-4300/16/3/1396
work_keys_str_mv	AT nicholasftravers infiniteexcessentropyprocesseswithcountablestategenerators AT jamespcrutchfield infiniteexcessentropyprocesseswithcountablestategenerators
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Infinite Excess Entropy Processes with Countable-State Generators

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