On Vershik’s Standardness Criterion and Tsirelson’s Notion of Cosiness

@inproceedings{mery2001OnVS,
  title={On Vershik’s Standardness Criterion and Tsirelson’s Notion of Cosiness},
  author={Michel {\'E}mery and Walter Schachermayer},
  year={2001}
}
Building on work done by A. Vershik some thirty years ago, the insight into different types of filtrations has recently seen important progress, due in particular to B. Tsirelson, and L. Dubins, J. Feldman, M. Smorodinsky, B. Tsirelson. Key concepts are the notions of a standard filtration (due to A. Vershik) and of a cosy filtration (due to B. Tsirelson). We investigate the relation between these two concepts and try to provide a comprehensive and self-contained presentation of the topic. 
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58 Citations
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58 Citations

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On Standardness and I-cosiness
The object of study of this work is the invariant characteristics of filtrations in discrete, negative time, pioneered by Vershik. We prove the equivalence between I-cosiness and standardness without…
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In the case of r n -adic filtrations, Vershik’s standardness criterion takes a particular form, hereafter called Vershik’s intermediate level criterion. This criterion, whose nature is combinatorial,…
The filtration of the split-words process
Smorodinsky and Laurent have initiated the study of the filtrations of split-word processes, in the framework of discrete negative time. For these filtrations, we show that Laurent’s sufficient…
Filtrations at the threshold of standardness
A. Vershik discovered that filtrations indexed by the non-positive integers may have a paradoxical asymptotic behaviour near the time $$-\infty $$, called non-standardness. For example, two dyadic…
Uniform Entropy Scalings of Filtrations
  • S. Laurent
  • Computer Science, Mathematics
    Lecture Notes in Mathematics
  • 2019
TLDR
Among the main results, it is proved that the scaled entropy of the filtration generated by the Vershik progressive predictions of a random variable is equal to the scaling entropy of this random variable.
Old and New Tools in the Theory of Filtrations
Vershik’s theory of standard filtered probability spaces and standardness criterion (established in the early seventies) are presented to a non-specialized audience and illustrated with examples.…
Filtrations of the Erased-Word Processes
TLDR
It is shown that the poly-adic filtration generated by such a process is standard and constructed with the help of Vershik's theory of filtrations in discrete negative time.
PR ] 1 A ug 2 01 2 Filtrations at the threshold of standardness
A. Vershik discovered that filtrations indexed by the non-positive integers may have a paradoxical asymptotic behaviour near the time −∞, called non-standardness. For example, two dyadic filtrations…
On certain probabilities equivalent to Wiener measure, d'Après Dubins, Feldman, Smorodinsky and Tsirelson
L. Dubins, J. Feldman, M. Smorodinsky and B. Tsirelson gave an example of an equivalent measure Q on standard Wiener space such that each adapted Q-Brownian motion generates a strictly smaller…
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