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* Corresponding author 1 IMB - Institut de Mathématiques de Bourgogne Dijon 2 LMV - Laboratoire de Mathématiques de Versailles 3 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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 : Variable length Markov chains Dynamical systems of the interval Dirichlet series Occurrences of words Probabilistic dynamical sources

Autor: Peggy Cénac - Brigitte Chauvin - Frédéric Paccaut - Nicolas Pouyanne -



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