# Almost sure limit theorems for dependent random variables

Banach Center Publications (2010)

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

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topMichał 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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