|Reference : On standardness and I-cosiness|
|Scientific journals : Article|
|Physical, chemical, mathematical & earth Sciences : Mathematics|
|On standardness and I-cosiness|
|Laurent, Stéphane [Université Catholique de Louvain - UCL > > > >]|
|Séminaire de Probabilités|
|[en] Standard filtrations ; Cosiness|
|[en] 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complements on the published and unpublished literature.
|IAP research network|
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