Issue |
ESAIM: PS
Volume 2, 1998
|
|
---|---|---|
Page(s) | 163 - 183 | |
DOI | https://doi.org/10.1051/ps:1998106 | |
Published online | 15 August 2002 |
An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law
(lanzinge@mathematik.uni-ulm.de)
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.
Résumé
Nous démontrons une loi forte des grands nombres pour des moyennes mouvantes de variables aléatoires indépendantes et équidistribuées avec une distribution sous-exponentielle. Ces variables aléatoires se comportent d'une façon qu'on peut considérer comme intermédiaire entre la loi classique et la loi forte d'Erdös-Rényi. Nous démontrons aussi que la différence avec la situation classique est causée par les variables les plus grandes.
Key words: Law of large numbers / almost sure convergence / exponential inequalities.
© EDP Sciences, SMAI, 1998
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