Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-26T17:34:56.853Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)