Elliptical symmetry and characterization of operator-stable and operator semi-stable measures. (English) Zbl 0549.60007

In this paper the author presents a characterization of an elliptically symmetric full-operator semi-stable measure on a finite dimensional real vector space V. As a corollary certain properties of full operator-stable measures are obtained. The paper concludes with a theorem giving necessary and sufficient conditions for a full infinitely divisible measure \(\mu\) on V to be (a) operator-stable or (b) strictly operator semi-stable, these conditions being framed in terms of the quasi- decomposability group of \(\mu\).
Reviewer: A.Dale


60B11 Probability theory on linear topological spaces
60E07 Infinitely divisible distributions; stable distributions
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