Filtrations at the threshold of standardness

@article{Ceillier2012FiltrationsAT,
title={Filtrations at the threshold of standardness},
author={Gael Ceillier and Christophe Leuridan},
journal={Probability Theory and Related Fields},
year={2012},
volume={158},
pages={785-808}
}
• Published 1 August 2012
• Mathematics
• Probability Theory and Related Fields
A. Vershik discovered that filtrations indexed by the non-positive integers may have a paradoxical asymptotic behaviour near the time $$-\infty$$, called non-standardness. For example, two dyadic filtrations with trivial tail $$\sigma$$-field are not necessarily isomorphic. Yet, from any essentially separable filtration indexed by the non-positive integers, one can extract a subsequence which is a standard filtration. In this paper, we focus on the non-standard filtrations which become…
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