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Almost sure limit theorems for dependent random variables

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Seweryn M.

Banach Center Publications

2010

tom 90

nr 1

171-178

For a sequence of dependent random variables $(X_{k})_{k∈ℕ}$ we consider a large class of summability methods defined by R. Jajte in \cite{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.

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1 Banach Center Publications

1 Seweryn M.

1 2010

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Almost sure limit theorems for dependent random variables