Filtrations at the threshold of standardness

  title={Filtrations at the threshold of standardness},
  author={Gael Ceillier and Christophe Leuridan},
  journal={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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Theory of decreasing sequences of measurable partitions
  • Algebra i Analiz,
  • 1994