Context trees, 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 uniqueness 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 : Tuesday, February 26, 2013 - 11:29:14 AM
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Peggy Cénac, Brigitte Chauvin, Frédéric Paccaut, Nicolas Pouyanne. Context trees, variable length Markov chains and dynamical sources.. Catherine Donati-Martin and Antoine Lejay and Alain Rouault. Séminaire de Probabilités XLIV, Springer, pp.1-39, 2012, Lecture Notes in Mathematics, 978-3-642-27460-2. ⟨10.1007/978-3-642-27461-9_1⟩. ⟨hal-00794627⟩



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