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December, 1979 On the Multivariate Law of the Iterated Logarithm
John A. Berning Jr.
Ann. Probab. 7(6): 980-988 (December, 1979). DOI: 10.1214/aop/1176994891

Abstract

A Hilbert space law of the iterated logarithm is proved which generalizes Kolmogorov's law for bounded random variables and which generalizes results of Teicher for unbounded random variables. The result for identically distributed random vectors is a consequence. The key idea is the requirement of the convergence of the average of the covariance operators.

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John A. Berning Jr.. "On the Multivariate Law of the Iterated Logarithm." Ann. Probab. 7 (6) 980 - 988, December, 1979. https://doi.org/10.1214/aop/1176994891

Information

Published: December, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0429.60003
MathSciNet: MR548892
Digital Object Identifier: 10.1214/aop/1176994891

Subjects:
Primary: 60B05
Secondary: 60F15 , 60G50

Keywords: Covariance operator , Law of the iterated logarithm , trace class operator

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 6 • December, 1979
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