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On standardness and I-cosiness

Authors
Publication Date
Keywords
  • Standard Filtrations
  • Cosiness
  • Physical
  • Chemical
  • Mathematical & Earth Sciences :: Mathematics [G03]
  • Physique
  • Chimie
  • Mathématiques & Sciences De La Terre :: Mathématiques [G03]

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derive the elementary properties of both these criteria, and to give a survey and some complements on the published and unpublished literature.

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