Variable length Markov chains and dynamical sources

Details Variable length Markov chains and dynamical sources Variable length Markov chains and dynamical sources

2010-07-18

arxiv.org/abs/1007.2986v1

Mathematics

Probability

45 pages, 15 figures

Scientific paper

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.

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