Paper detail

On the mixing structure of stationary increment and self-similar symmetric α-stable processes

Mixed moving average processes appear in the ergodic decomposition of stationary symmetric α-stable (SαS) processes. They correspond to the dissipative part of "deterministic" flows generating SαS processes (Rosinski, 1995). Along these lines we study stationary increment and self-similar SαS processes. Since the classes of stationary increment and self-similar processes can be embedded into the class of stationary processes by the Masani and Lamperti transformations, respectively, we characterize these classes of SαS processes in terms of nonsingular flows and the related cocycles. We illustrate this approach considering various examples of self-similar mixed moving average SαS processes introduced in (Surgailis, Rosinski, Mandrekar and Cambanis, 1992).