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Relative stability, characteristic functions and stochastic compactness

Part of: Limit theorems Stochastic processes Distribution theory - Probability

Published online by Cambridge University Press:  09 April 2009

R. A. Maller
R. A. Maller
Affiliation:
CSIRO Division of Mathematics and Statics, Melbourne, Australia
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Abstract

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A recent result of Rogozin on the relative stability of a distribution function is extended, by giving equivalences for relative stability in terms of truncated moments of the distribution and in terms of the real and imaginary parts of the characteristic function. As an application, the known results on centering distributions in the domain of attraction of a stable law are extended to the case of stochastically compact distributions.

MSC classification

Secondary: 60F05: Central limit and other weak theorems 60E10: Characteristic functions; other transforms 60G50: Sums of independent random variables; random walks

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 4 , December 1979 , pp. 499 - 509
Copyright
Copyright © Australian Mathematical Society 1979

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