The Annals of Probability

Some Extensions of the LIL Via Self-Normalizations

Philip Griffin and James Kuelbs

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Abstract

We study some generalizations of the LIL when self-normalizations are used. Two particular results proved are: (1) an extension of the Kolmogorov-Erdos test for partial sums of symmetric i.i.d. random variables having finite second moments; this result eliminates distinctions required when nonrandom normalizers are used and $E(X^2I(|X| > t))$ is not $O((L_2t)^{-1})$, and (2) an extension of a universal bounded LIL of Marcinkiewicz to nonsymmetric random variables. An interesting corollary of this work is a short new proof of the classical LIL avoiding truncation methods.

Article information

Source
Ann. Probab., Volume 19, Number 1 (1991), 380-395.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990551

Digital Object Identifier
doi:10.1214/aop/1176990551

Mathematical Reviews number (MathSciNet)
MR1085343

Zentralblatt MATH identifier
0722.60028

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems

Keywords
Law of the iterated logarithm Kolmogorov-Erdos test upper and lower functions self-normalizations

Citation

Griffin, Philip; Kuelbs, James. Some Extensions of the LIL Via Self-Normalizations. Ann. Probab. 19 (1991), no. 1, 380--395. doi:10.1214/aop/1176990551. https://projecteuclid.org/euclid.aop/1176990551


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