THE SPECTRAL REPRESENTATION OF STABLE PROCESSES - HARMONIZABILITY AND REGULARITY

We show that symmetric α-stable moving average processes are not harmonizable. However, we show that a concept of generalized spectrum holds for all Lp-bounded processes O<p<-2. In cape p=2, generalized spectrum is a measure and the classical representation follows. For strongly harmonizable symmetric α-stable processes we derive necessary and sufficient conditions for the regularity and the singularity for 0<α≦2, using known results on the invariant subspaces. We also get Cramér-Wold decomposition for the case 0<α≦2. © 1990 Springer-Verlag.