Search results for "Occurrences of words"

showing 2 items of 2 documents

Context Trees, Variable Length Markov Chains and Dynamical Sources

2012

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 uniqueness 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 genera…

Discrete mathematicsPure mathematicsStationary distributionMarkov chain010102 general mathematicsProbabilistic dynamical sourcesProbabilistic logicContext (language use)Information theoryVariable length Markov chains01 natural sciencesMeasure (mathematics)Occurrences of words[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]010104 statistics & probabilitysymbols.namesakesymbolsUniquenessDynamical systems of the intervalDirichlet series0101 mathematics[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]Dirichlet seriesMathematics
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Variable length Markov chains and dynamical sources

2010

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 gener…

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
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