Null flows, positive flows and the structure of stationary symmetric stable processes

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73658This paper elucidates the connection between stationary symmetric alpha-stable processes with 0<alpha<2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that a necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.Probability60G10, 60G52Null flows, positive flows and the structure of stationary symmetric stable processestext