ABSTRACT
A reader familiar with the spectral theory of stationary Gaussian processes will recall that every stationary Gaussian process, continuous in probability, can be so represented and hence is harmonizable. Nevertheless, the class of stationary harmonizable a-stable processes is of importance and it deserves a careful study. This chapter considers stationary real harmonizable processes. Although these processes share properties with stationary sub-Gaussian processes, it is shown that the two classes are "almost" disjoint. The chapter defines that Complex-valued SaS random measures are analogous to the real random measures, but they are, naturally, a little more complicated. It develops conditions for the stationarity of the real- and complex-valued harmonizable SaS processes.
