A characterization and moving average representation for stable harmonizable processes

M. Nikfar and A. Reza Soltani

International Journal of Stochastic Analysis, 1996, vol. 9, 1-8

Abstract:

In this paper we provide a characterization for symmetric α -stable harmonizable processes for 1 < α ≤ 2 . We also deal with the problem of obtaining a moving average representation for stable harmonizable processes discussed by Cambanis 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 α -stable random variables, 1 < α ≤ 2 , then there is a function k ∈ L 2 ( λ ) ( λ is the Lebesgue measure) and a certain symmetric- α -stable random measure Y for which ∫ − ∞ ∞ e i t x d Z ( x ) = ∫ − ∞ ∞ k ( t − s ) d Y ( s ) , t ∈ R , if and only if Z ( A ) = 0 whenever λ ( A ) = 0 . Our method is to view S α S processes with parameter space R as S α S processes whose parameter spaces are certain L β spaces.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:324107

DOI: 10.1155/S1048953396000251

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