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.
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Submitted on : Saturday, July 17, 2010 - 7:54:14 AM
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Peggy Cénac, Brigitte Chauvin, Frédéric Paccaut, Nicolas Pouyanne. Variable length Markov chains and dynamical sources. 2010. ⟨hal-00503150⟩

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