Variable length Markov chains and dynamical sources
Abstract
Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sources is studied. We establish a probabilistic frame for context trees and VLMC and we prove that any VLMC is a dynamical source for which we explicitly build the mapping. On two examples, the ``comb'' and the ``bamboo blossom'', we find a necessary and sufficient condition for the existence and the unicity of a stationary probability measure for the VLMC. These two examples are detailed in order to provide the associated Dirichlet series as well as the generating functions of word occurrences.
Keywords
Cite
@article{arxiv.1007.2986,
title = {Variable length Markov chains and dynamical sources},
author = {Peggy Cénac and Brigitte Chauvin and Frédéric Paccaut and Nicolas Pouyanne},
journal= {arXiv preprint arXiv:1007.2986},
year = {2010}
}
Comments
45 pages, 15 figures