Open Access
February, 1983 The Domain of Normal Attraction of an Operator-Stable Law
William N. Hudson, J. David Mason, Jerry Alan Veeh
Ann. Probab. 11(1): 178-184 (February, 1983). DOI: 10.1214/aop/1176993667


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.


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William N. Hudson. J. David Mason. Jerry Alan Veeh. "The Domain of Normal Attraction of an Operator-Stable Law." Ann. Probab. 11 (1) 178 - 184, February, 1983.


Published: February, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0504.60007
MathSciNet: MR682808
Digital Object Identifier: 10.1214/aop/1176993667

Primary: 60E05

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

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • February, 1983
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