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IPM
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YEARS OLD

“School of Mathematics”

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Paper   IPM / M / 464
School of Mathematics
  Title:   A characterization theorem for stable random measures
  Author(s):  A. R. Soltani
  Status:   Published
  Journal: Stochastic Anal. Appl.
  No.:  2
  Vol.:  18
  Year:  2000
  Pages:   299-308
  Supported by:  IPM
  Abstract:
Let (S, ||  ||) be a Banach space of jointly symmetric α-stable random variables and let P be the δ-ring of Borel sets of finite ν measure, where ν is a regular measure in the real line. In this paper we identify every stable random measure Ψ:P→ (S,||  ||), Ψ << ν, by a vector measure F : PLα (μ). This leads to a method for identifying spectral domain of a certain class of stable processes including harmonizable processes.

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