2018/07/03 by Cénac, Peggy, Chauvin, Brigitte, Paccaut, Frédéric +1
#60C05 #60G10 #60J05 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1807.01075
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.