On vershikian and I-cosy random variables and filtrations
(2011) Theory of Probability and Its Applications — Vol. 55, n° 1, p. 54-76 (2011)
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- Abstract
- We prove that the equivalence between Vershik's standardness criterion and the Icosiness criterion for a filtration in discrete, negative time holds separately for each random variable. This gives a strengthening and a more direct proof of the global equivalence between these two criteria. We also provide more elementary original propositions on Vershik's standardness criterion, while emphasizing that similar statements for I-cosiness are sometimes not so obvious. © 2011 Society for Industrial and Applied Mathematics.
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Laurent, S. (2011). On vershikian and I-cosy random variables and filtrations. Theory of Probability and Its Applications, 55(1), 54-76. https://doi.org/10.1137/S0040585X97984656 (Original work published 2011)