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Preprints, Working Papers, ... Year : 2014

Uniform entropy scalings of filtrations

Stéphane Laurent
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Abstract

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 \emph{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.
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Dates and versions

hal-01006337 , version 1 (15-06-2014)
hal-01006337 , version 2 (03-07-2014)
hal-01006337 , version 3 (22-06-2015)
hal-01006337 , version 4 (15-01-2016)
hal-01006337 , version 5 (16-08-2016)

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  • HAL Id : hal-01006337 , version 1

Cite

Stéphane Laurent. Uniform entropy scalings of filtrations. 2014. ⟨hal-01006337v1⟩
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