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April, 1980 Limit Theorems Without Moment Hypotheses for Sums of Independent Random Variables
R. J. Tomkins
Ann. Probab. 8(2): 314-324 (April, 1980). DOI: 10.1214/aop/1176994779

Abstract

Let $\{S_n\}$ be the partial sums of a sequence of independent random variables and let $\{a_n\}$ be a nondecreasing, divergent real sequence. Necessary and sufficient conditions for $\lim \sup_{n\rightarrow\infty}S_n/a_n < \infty$ a.s. are given under mild conditions on $\{S_n\}$; these conditions do not involve the existence of any moments. These results are employed to widen the scope of the law of the iterated logarithm.

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R. J. Tomkins. "Limit Theorems Without Moment Hypotheses for Sums of Independent Random Variables." Ann. Probab. 8 (2) 314 - 324, April, 1980. https://doi.org/10.1214/aop/1176994779

Information

Published: April, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0432.60034
MathSciNet: MR566596
Digital Object Identifier: 10.1214/aop/1176994779

Subjects:
Primary: 60F15
Secondary: 60G50

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 2 • April, 1980
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