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

ESAIM: Probability and Statistics (1)

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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
Hartmut Lanzinger
Journal:

ESAIM: Probability and Statistics / Volume 2 / 1998

Published online by Cambridge University Press:

15 August 2002, pp. 163-183

Print publication:

1998
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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.