The Annals of Probability

The Domain of Normal Attraction of an Operator-Stable Law

William N. Hudson, J. David Mason, and Jerry Alan Veeh

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Abstract

The idea of the domain of normal attraction was earlier extended to probabilities on a finite-dimensional inner-product space. We obtain a necessary and sufficient condition that a probability be in the domain of normal attraction of a given probability in terms of their covariance operators and of a limit involving the Levy measure. This condition appears to be the natural generalization of the corresponding univariate condition. We also show that the domains of normal attraction of two probabilities are either the same or disjoint, with a condition that is necessary and sufficient for them to be the same.

Article information

Source
Ann. Probab., Volume 11, Number 1 (1983), 178-184.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993667

Digital Object Identifier
doi:10.1214/aop/1176993667

Mathematical Reviews number (MathSciNet)
MR682808

Zentralblatt MATH identifier
0504.60007

JSTOR
links.jstor.org

Subjects
Primary: 60E05: Distributions: general theory

Keywords
Operator-stable laws multivariate stable laws central limit theorem domain of normal attraction

Citation

Hudson, William N.; Mason, J. David; Veeh, Jerry Alan. The Domain of Normal Attraction of an Operator-Stable Law. Ann. Probab. 11 (1983), no. 1, 178--184. doi:10.1214/aop/1176993667. https://projecteuclid.org/euclid.aop/1176993667


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