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arXiv · 1807.01075

Characterization of stationary probability measures for Variable Length Markov Chains

Peggy Cénac·Brigitte Chauvin·Frédéric Paccaut·Nicolas Pouyanne
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Abstract

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.

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Peggy Cénac, Brigitte Chauvin, Frédéric Paccaut, Nicolas Pouyanne. 2018-07-03. Characterization of stationary probability measures for Variable Length Markov Chains. https://arxiv.org/abs/1807.01075

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