Complementability and maximality in different contexts: ergodic theory, Brownian and poly-adic ltrations

Christophe Leuridan (1)

1 IF - Institut Fourier

The notions of complementability and maximality were introduced in 1974 by Ornstein and Weiss in the context of the automorphisms of a probability space, in 2008 by Brossard and Leuridan in the context of the Brownian ltrations, and in 2017 by Leuridan in the context of the poly-adic ltrations indexed by the non-positive integers. We present here some striking analogies and also some dierences existing between these three contexts.

Mots clés: exchange property; Brownian ltrations; the non-positive integers; poly-adic ltrations; Automorphisms of Lebesgue spaces; factors; entropy; ltrations indexed by; immersed; ltrations; complementability; maximality

Domaines: Probabilités [math.PR]; Mathématiques [math]

Christophe Leuridan. Complementability and maximality in different contexts: ergodic theory, Brownian and poly-adic ltrations. 2017. ⟨hal-01560477v2⟩