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

Łuczak, A.

Ann. Probab. 12, 1217-1223 (1984).

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

MSC:

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

Keywords:

full-operator semi-stable measure; infinitely divisible measure; quasi- decomposability group