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

Lanzinger, Hartmut. "An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law." ESAIM: Probability and Statistics 2 (2010): 163-183. <http://eudml.org/doc/197735>.

@article{Lanzinger2010,
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. },
author = {Lanzinger, Hartmut},
journal = {ESAIM: Probability and Statistics},
keywords = {Law of large numbers / almost sure convergence / exponential inequalities. ; almost sure limit theorem; increments of partial sums; Erdős-Rényi-Shepp law},
language = {eng},
month = {3},
pages = {163-183},
publisher = {EDP Sciences},
title = {An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law},
url = {http://eudml.org/doc/197735},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Lanzinger, Hartmut
TI - An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 2
SP - 163
EP - 183
AB - 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.
LA - eng
KW - Law of large numbers / almost sure convergence / exponential inequalities. ; almost sure limit theorem; increments of partial sums; Erdős-Rényi-Shepp law
UR - http://eudml.org/doc/197735
ER -