## The Annals of Probability

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

### The Domain of Normal Attraction of an Operator-Stable Law

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

#### 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