Non-sequential recursive pair substitutions and numerical entropy estimates in symbolic dynamical systems
Statistical Mechanics
2009-07-21 v2 Dynamical Systems
Statistics Theory
Chaotic Dynamics
Statistics Theory
Abstract
We numerically test the method of non-sequential recursive pair substitutions to estimate the entropy of an ergodic source. We compare its performance with other classical methods to estimate the entropy (empirical frequencies, return times, Lyapunov exponent). We considered as a benchmark for the methods several systems with different statistical properties: renewal processes, dynamical systems provided and not provided with a Markov partition, slow or fast decay of correlations. Most experiments are supported by rigorous mathematical results, which are explained in the paper.
Cite
@article{arxiv.0809.1342,
title = {Non-sequential recursive pair substitutions and numerical entropy estimates in symbolic dynamical systems},
author = {Lucio M. Calcagnile and Stefano Galatolo and Giulia Menconi},
journal= {arXiv preprint arXiv:0809.1342},
year = {2009}
}
Comments
v2: modifications to the numerical part and minor other changes