Almost sure limit theorems for dependent random variables

• Autorzy: Michał Seweryn
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A25: Ergodicity, mixing, rates of mixing
• 60F15: Strong theorems
• 60G42: Martingales with discrete parameter

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 90
• Numer: 1
• Strony: 171-178

Daty

wydano

2010

Twórcy

autor

Michał Seweryn

• Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Identyfikatory

DOI

10.4064/bc90-0-11