Uniform entropy scalings of filtrations
Résumé
We study Vershik and Gorbulsky's notion of entropy scalings for filtrations in the particular case when the scaling is not epsilon-dependent, and is then termed as uniform scaling. Our main result states that the scaled entropy of the filtration generated by the Vershik progressive predictions of a random variable is equal to the scaled entropy of this random variable. Standardness of a filtration is the case when the scaled entropy with a constant scaling is zero, thus our results generalize some known results about standardness. As an example we derive a proper uniform entropy scaling for a next-jump time filtration. As a side note, we use the example of the next-jump time filtrations to write down a case study of Vershik's theory of intrinsic topology on Bratteli graphs.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)