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An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law

Published online by Cambridge University Press:  15 August 2002

Hartmut Lanzinger
Hartmut Lanzinger*
Affiliation:
(lanzinge@mathematik.uni-ulm.de)
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Abstract

We prove a strong law of large numbers for moving averages of independent, identically distributed random variables with certain subexponential distributions. These random variables show a behavior that can be considered intermediate between the classical strong law and the Erdös-Rényi law. We further show that the difference from the classical behavior is due to the influence of extreme terms.

Keywords

Law of large numbers / almost sure convergence / exponential inequalities.

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 2 , 1998 , pp. 163 - 183
Copyright
© EDP Sciences, SMAI, 1998

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