On Vershikian and I-cosy random variables and filtrations@@@On Vershikian and I-cosy random variables and filtrations

@inproceedings{Laurent2010OnVA,
  title={On Vershikian and I-cosy random variables and filtrations@@@On Vershikian and I-cosy random variables and filtrations},
  author={St{\'e}phane Laurent},
  year={2010}
}
4 Citations
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.
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
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

References

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Espaces probabilisés filtrés : de la théorie de Vershik au mouvement brownien, via des idées de Tsirelson
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and
Triple Points: From Non-Brownian Filtrations to Harmonic Measures
Abstract. ((Without abstract))
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
On Vershik’s Standardness Criterion and Tsirelson’s Notion of Cosiness
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.