Maharam extension and spectral representation of stable processes
Résumé
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.
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