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.
"Maharam extension and stationary stable processes." Ann. Probab. 40 (3) 1357 - 1374, May 2012. https://doi.org/10.1214/11-AOP671