Symmetry groups in d-space

Mark M. Meerschaert and Jeery Alan Veeh

Statistics & Probability Letters, 1995, vol. 22, issue 1, 1-6

Abstract: We show that any finite-dimensional compact Lie group is isomorphic to the symmetry group of a full probability measure. The novelty of our proof is that an explicit formula for the measure and its support is given in terms of the Lie group. We also construct a full operator stable probability measure whose symmetry group has as its tangent space the tangent space of a given group. This provides a method for constructing an operator stable probability measure having a specified collection of exponents. A characterization of the compact groups of operators on a finite-dimensional space which can be the symmetry group of a full probability measure on that same space is given.

Keywords: Symmetry; group; Full; probability; measure; Operator; stable; probability; measure (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (3)

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