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Séminaire de Probabilités XLIII pp 127–186Cite as

On Standardness and I-cosiness

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Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2006))

Abstract

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 using Vershik’s standardness criterion. The equivalence between I-cosiness and productness for homogeneous filtrations is further investigated by showing that the I-cosiness criterion is equivalent to Vershik’s first level criterion separately for each random variable. We also aim to derive the elementary properties of both these criteria, and to give a survey and some complements on the published and unpublished literature.

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Acknowledgements

Financial support from the IAP research network (grant nr. P6/03 of the Belgian government, Belgian Science Policy) is gratefully acknowledged. I am also indebted to M. Émery for helpful and encouraging comments and suggestions on earlier drafts of this paper.

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  1. Stéphane Laurent

    Present address: Université de Strasbourg, IRMA, UMR 7501, 7 rue René-Descartes, 67084, Strasbourg Cedex, France

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  1. Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Stéphane Laurent

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  1. Stéphane Laurent
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Correspondence to Stéphane Laurent .

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Editors and Affiliations

  1. Lab. de Probabilités et Modèles Aléatoir, Université Pierre et Marie Curie, place Jussieu 4, Paris Cedex 05, 75252, France

    Catherine Donati-Martin

  2. IECN, Campus scientifique, BP 239, Nancy-Université, INRIA, Vandoeuvre-lès-Nancy, 54506, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des Etats-Unis 45, Versailles, 78035, France

    Alain Rouault

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Laurent, S. (2011). On Standardness and I-cosiness. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIII. Lecture Notes in Mathematics(), vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15217-7_5

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