6533b870fe1ef96bd12d0564

RESEARCH PRODUCT

Variable length Markov chains and dynamical sources

Peggy Cénac Brigitte Chauvin Frédéric Paccaut Nicolas Pouyanne

subject

MSC 60J05 MSC 37E05[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Probability (math.PR)[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]Probabilistic dynamical sources[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)Variable length Markov chainsOccurrences of words[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]60J05 37E05FOS: MathematicsMathematics - Dynamical SystemsDynamical systems of the intervalDirichlet series[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]Mathematics - Probability

description

Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sources is studied. We establish a probabilistic frame for context trees and VLMC and we prove that any VLMC is a dynamical source for which we explicitly build the mapping. On two examples, the ``comb'' and the ``bamboo blossom'', we find a necessary and sufficient condition for the existence and the unicity of a stationary probability measure for the VLMC. These two examples are detailed in order to provide the associated Dirichlet series as well as the generating functions of word occurrences.

yearjournalcountryeditionlanguage
2010-07-18
https://hal.science/hal-00724553