# Almost sure limit theorems for dependent random variables

• Volume: 90, Issue: 1, page 171-178
• ISSN: 0137-6934

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## Abstract

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For a sequence of dependent random variables ${\left({X}_{k}\right)}_{k\in ℕ}$ we consider a large class of summability methods defined by R. Jajte in [jaj] as follows: For a pair of real-valued nonnegative functions g,h: ℝ⁺ → ℝ⁺ we define a sequence of “weighted averages” $1/g\left(n\right){\sum }_{k=1}^{n}\left({X}_{k}\right)/h\left(k\right)$, where g and h satisfy some mild conditions. We investigate the almost sure behavior of such transformations. We also take a close look at the connection between the method of summation (that is the pair of functions (g,h)) and the coefficients that measure dependence between the random variables.

## How to cite

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Michał Seweryn. "Almost sure limit theorems for dependent random variables." Banach Center Publications 90.1 (2010): 171-178. <http://eudml.org/doc/282542>.

@article{MichałSeweryn2010,
abstract = {For a sequence of dependent random variables $(X_\{k\})_\{k∈ℕ\}$ we consider a large class of summability methods defined by R. Jajte in [jaj] as follows: For a pair of real-valued nonnegative functions g,h: ℝ⁺ → ℝ⁺ we define a sequence of “weighted averages” $1/g(n) ∑_\{k=1\}^\{n\} (X_\{k\})/h(k)$, where g and h satisfy some mild conditions. We investigate the almost sure behavior of such transformations. We also take a close look at the connection between the method of summation (that is the pair of functions (g,h)) and the coefficients that measure dependence between the random variables.},
author = {Michał Seweryn},
journal = {Banach Center Publications},
keywords = {strong law of large numbers; mixing sequences; martingale differences},
language = {eng},
number = {1},
pages = {171-178},
title = {Almost sure limit theorems for dependent random variables},
url = {http://eudml.org/doc/282542},
volume = {90},
year = {2010},
}

TY - JOUR
AU - Michał Seweryn
TI - Almost sure limit theorems for dependent random variables
JO - Banach Center Publications
PY - 2010
VL - 90
IS - 1
SP - 171
EP - 178
AB - For a sequence of dependent random variables $(X_{k})_{k∈ℕ}$ we consider a large class of summability methods defined by R. Jajte in [jaj] as follows: For a pair of real-valued nonnegative functions g,h: ℝ⁺ → ℝ⁺ we define a sequence of “weighted averages” $1/g(n) ∑_{k=1}^{n} (X_{k})/h(k)$, where g and h satisfy some mild conditions. We investigate the almost sure behavior of such transformations. We also take a close look at the connection between the method of summation (that is the pair of functions (g,h)) and the coefficients that measure dependence between the random variables.
LA - eng
KW - strong law of large numbers; mixing sequences; martingale differences
UR - http://eudml.org/doc/282542
ER -

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