Classes of mixing stable processes

Abstract

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.