Infinite Excess Entropy Processes with Countable-State Generators
Information Theory
2011-11-16 v1 Statistical Mechanics
math.IT
Probability
Chaotic Dynamics
Abstract
We present two examples of finite-alphabet, infinite excess entropy processes generated by invariant hidden Markov models (HMMs) with countable state sets. The first, simpler example is not ergodic, but the second is. It appears these are the first constructions of processes of this type. Previous examples of infinite excess entropy processes over finite alphabets admit only invariant HMM presentations with uncountable state sets.
Cite
@article{arxiv.1111.3393,
title = {Infinite Excess Entropy Processes with Countable-State Generators},
author = {Nicholas F. Travers and James P. Crutchfield},
journal= {arXiv preprint arXiv:1111.3393},
year = {2011}
}
Comments
13 pages, 3 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/ieepcsg.htm