Maharam extension and stationary stable processes

TL;DR

This paper reinterprets stationary stable processes through Maharam systems, revealing structural insights and ergodic properties by analyzing their self-similarity at the level of the Lévy measure.

Contribution

It introduces a novel perspective by linking stationary stable processes to Maharam systems, providing new structural and ergodic results.

Findings

Structural characterization of stationary stable processes

Connection between self-similarity and Maharam systems

Ergodic properties derived from this interpretation

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.