Almost sure limit theorems for dependent random variables

Volume 90 / 2010

Micha/l Seweryn Banach Center Publications 90 (2010), 171-178 MSC: Primary 60F15; Secondary 60G42, 37A25. DOI: 10.4064/bc90-0-11


For a sequence of dependent random variables $(X_{k})_{k\in \mathbb{N}}$ 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 $g,h:\mathbb{R}^{+}\rightarrow \mathbb{R}^{+}$ we define a sequence of “weighted averages” $\frac{1}{g(n)}\sum_{k=1}^{n}\frac{X_{k}}{h(k)}$, 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.


  • Micha/l SewerynFaculty of Mathematics and Computer Science
    University of Łódź
    Banacha 22
    90-238 Łódź, Poland

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