A characterization and moving average representation for stable harmonizable processes
In this paper we provide a characterization for symmetric -stable harmonizable processes for . We also deal with the problem of obtaining a moving average representation for stable harmonizable processes discussed by Cambanis and Soltani , Makegan and Mandrekar , and Cambanis and Houdre . More precisely, we prove that if is an independently scattered countable additive set function on the Borel field with values in a Banach space of jointly symmetric -stable random variables, , then there is a function ( is the Lebesgue measure) and a certain symmetric--stable random measure for which , if and only if whenever . Our method is to view processes with parameter space as processes whose parameter spaces are certain spaces.