Characterization of stationary probability measures for Variable Length Markov Chains
Probability
2018-07-04 v1
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.
Keywords
Cite
@article{arxiv.1807.01075,
title = {Characterization of stationary probability measures for Variable Length Markov Chains},
author = {Peggy Cénac and Brigitte Chauvin and Frédéric Paccaut and Nicolas Pouyanne},
journal= {arXiv preprint arXiv:1807.01075},
year = {2018}
}
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32 pages