Infinite Excess Entropy Processes with Countable-State Generators

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
Description
Summary: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.
ISSN:1099-4300

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