Uniform entropy scalings of filtrations

Stéphane Laurent (1)

1 Chercheur indépendant

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 a uniform scaling. Among our main results, we prove 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 a case-study we consider a family of next-jump time filtrations. We also provide some results about the entropy of poly-adic filtrations, rephrasing or generalizing some old results.

Mots clés: filtration; standardness; entropy

Domaines: Probabilités [math.PR]; Théorie de l'information et codage [math.IT]; Systèmes dynamiques [math.DS]

Stéphane Laurent. Uniform entropy scalings of filtrations. 2016. ⟨hal-01006337v5⟩