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October, 1978 The Law of the Iterated Logarithm and Upper-Lower Class Tests for Partial Sums of Stationary Gaussian Sequences
Tze Leung Lai, William Stout
Ann. Probab. 6(5): 731-750 (October, 1978). DOI: 10.1214/aop/1176995425

Abstract

Herein, laws of the iterated logarithm and various upper-lower class refinements are established for partial sums of stationary Gaussian random variables. These stationary Gaussian random variables are not necessarily in any sense weakly dependent. For example, if the random variables are nonnegatively correlated, then the upper half of the law of the iterated logarithm holds. Under more restrictive, but still quite general hypotheses, an upper-lower class test which classifies all monotone sequences $\{\phi(n)\}$ is established.

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Tze Leung Lai. William Stout. "The Law of the Iterated Logarithm and Upper-Lower Class Tests for Partial Sums of Stationary Gaussian Sequences." Ann. Probab. 6 (5) 731 - 750, October, 1978. https://doi.org/10.1214/aop/1176995425

Information

Published: October, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0403.60032
MathSciNet: MR494437
Digital Object Identifier: 10.1214/aop/1176995425

Subjects:
Primary: 60F15
Secondary: 60G15, 60G50

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 5 • October, 1978
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