Maharam extension and stationary stable processes

Abstract

We give a second look at stationary stable processes by interpreting the self-similar property at the level of the L\'evy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences.Comment: Published in at http://dx.doi.org/10.1214/11-AOP671 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org