On Vershikian and I-Cosy Random Variables and Filtrations

@article{Laurent2011OnVA,
title={On Vershikian and I-Cosy Random Variables and Filtrations},
author={St{\'e}phane Laurent},
journal={Theory of Probability and Its Applications},
year={2011},
volume={55},
pages={54-76}
}
• S. Laurent
• Published 7 March 2011
• Mathematics
• Theory of Probability and Its Applications
We prove that the equivalence between Vershik's standardness criterion and the I-cosiness 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.

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