A characterization and moving average representation for stable harmonizable processes

In this paper we provide a characterization for symmetric c-stable harmoniz-able processes for 1 < c < 2. We also deal with the problem of obtaining a mov-ing average representation for stable harmonizable processes discussed by Cam-banis and Soltani [3], Makegan and Mandrekar [9], and Cambanis and Houdre [2]. More precisely, we prove that if Z is an independently scattered countable additive set function on the Borel field with values in a Banach space of jointly symmetric c-stable random variables, 1 < c <2, then there is a function k E L2($) (. is the Lebesgue measure) and a certain symmetric-a-stable random measure Y for which if and only if Z(A)- 0 whenever $(A)- 0. Our method is to view SS process-es with parameter space R as SS processes whose parameter spaces are certain L3 spaces