Every measurable stationary α-stable process with 0<α<2 can be related to a non-singular flow on a σ-finite measure space. We establish the relationship between properties of the flow and mixing of the stationary stable process. We provide the first example of a mixing stationary stable process corresponding to a conservative flow. We show further the connection between the expected return time of the flow to sets of finite positive measure and the mixing properties of the process.
"Classes of mixing stable processes." Bernoulli 2 (4) 365 - 377, December 1996.