Pré-Publication, Document De Travail Année : 2018

Characterization of stationary probability measures for Variable Length Markov Chains

Résumé

By introducing a key combinatorial structure for words produced by a Variable Length Markov Chain (VLMC), the longest internal suffix, precise characterizations of existence and uniqueness of a stationary probability measure for a VLMC chain are given. These characterizations turn into necessary and sufficient conditions for VLMC associated to a subclass of probabilised context trees: the shift-stable context trees. As a by-product, we prove that a VLMC chain whose stabilized context tree is again a context tree has at most one stationary probability measure. MSC 2010: 60J05, 60C05, 60G10.

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relationship_isVariantFormatOf hal-02462959 Preprint Peggy Cénac, Brigitte Chauvin, Frédéric Paccaut, Nicolas Pouyanne. Characterization of stationary probability measures for Variable Length Markov Chains. 2020. ⟨hal-02462959⟩

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hal-01829562 , version 1 (04-07-2018)

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Peggy Cénac, Brigitte Chauvin, Frédéric Paccaut, Nicolas Pouyanne. Characterization of stationary probability measures for Variable Length Markov Chains. 2018. ⟨hal-01829562⟩
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