# Variable length Markov chains and dynamical sources

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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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https://hal.archives-ouvertes.fr/hal-00503150
Contributor : Nicolas Pouyanne <>
Submitted on : Saturday, July 17, 2010 - 7:54:14 AM
Last modification on : Wednesday, January 23, 2019 - 2:39:26 PM
Long-term archiving on : Tuesday, October 23, 2012 - 10:30:37 AM

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• HAL Id : hal-00503150, version 1

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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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