The Annals of Probability

Operator-Stable Laws: Multiple Exponents and Elliptical Symmetry

J. P. Holmes, William N. Hudson, and J. David Mason

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Abstract

We characterize the class of linear operators on a finite dimensional inner product space which are the exponents of a full operator-stable law. This answers a question of Paulauskas [6] concerning those operator-stable laws whose characteristic functions are the exponential of quadratic forms. The symmetry group of such laws must be conjugate to the group of all orthogonal transformations on the space.

Article information

Source
Ann. Probab., Volume 10, Number 3 (1982), 602-612.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993770

Digital Object Identifier
doi:10.1214/aop/1176993770

Mathematical Reviews number (MathSciNet)
MR659531

Zentralblatt MATH identifier
0488.60026

JSTOR
links.jstor.org

Subjects
Primary: 60E05: Distributions: general theory

Keywords
Operator-stable distributions multivariate stable laws central limit theorem

Citation

Holmes, J. P.; Hudson, William N.; Mason, J. David. Operator-Stable Laws: Multiple Exponents and Elliptical Symmetry. Ann. Probab. 10 (1982), no. 3, 602--612. doi:10.1214/aop/1176993770. https://projecteuclid.org/euclid.aop/1176993770


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