Maharam extension and spectral representation of stable processes

Emmanuel Roy (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We give a second look at stable processes (especially stationary) by interpreting the self-similar property at the level of the Lévy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences. As a byproduct, we obtain a “stable processes” proof of Banach-Lamperti Theorem for \alpha<2.

Mots clés: Stable stationary processes; Maharam system; ergodic properties

Domaines: Systèmes dynamiques [math.DS]; Probabilités [math.PR]

Emmanuel Roy. Maharam extension and spectral representation of stable processes. 2010. ⟨hal-00443893v2⟩