6533b872fe1ef96bd12d2e74

RESEARCH PRODUCT

Characterization of stationary probability measures for Variable Length Markov Chains

Peggy CénacBrigitte ChauvinFrédéric PaccautNicolas Pouyanne

subject

[MATH.MATH-PR]Mathematics [math]/Probability [math.PR][MATH.MATH-PR] Mathematics [math]/Probability [math.PR]60J05 60C05 60G10Probability (math.PR)FOS: MathematicsMathematics - Probability

description

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.

yearjournalcountryeditionlanguage
2020-01-31
https://hal.science/hal-01829562