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.
Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.