Maharam extension and stationary stable processes

Emmanuel Roy (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We give a second look at stationary stable processes 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.

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

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

Emmanuel Roy. Maharam extension and stationary stable processes. Annals of Probability, 2012, 40 (3), pp.1357-1374. ⟨10.1214/11-AOP671⟩. ⟨hal-00443893v4⟩