# 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 (2010)

- Volume: 2, page 163-183
- ISSN: 1292-8100

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topLanzinger, 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 -

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