On standardness and I-cosiness

Laurent, Stéphane
(2011) Lecture Notes in Mathematics — Vol. 2006, p. 127-186 (2011)

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  • Laurent, StéphaneUCLouvain
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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derive the elementary properties of both these criteria, and to give a survey and some complements on the published and unpublished literature. © 2011 Springer-Verlag Berlin Heidelberg.
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Laurent, S. (2011). On standardness and I-cosiness. Lecture Notes in Mathematics, 2006, 127-186. https://doi.org/10.1007/978-3-642-15217-7_5 (Original work published 2011)