One sided strong laws for random variables with infinite mean

André Adler

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Displaying similar documents to “One sided strong laws for random variables with infinite mean”

Inequalities and limit theorems for random allocations

Istvan Fazekas, Alexey Chuprunov, Jozsef Turi (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Random allocations of balls into boxes are considered. Properties of the number of boxes containing a fixed number of balls are studied. A moment inequality is obtained. A merge theorem with Poissonian accompanying laws is proved. It implies an almost sure limit theorem with a mixture of Poissonian laws as limiting distribution. Almost sure versions of the central limit theorem are obtained when the parameters are in the central domain.

Inequalities and limit theorems for random allocations

István Fazekas, Alexey Chuprunov, József Túri (2011)

Annales UMCS, Mathematica

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An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law

Hartmut Lanzinger (2010)

ESAIM: Probability and Statistics

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We prove a strong law of large numbers for moving averages of independent, identically distributed random variables with certain subexponential distributions. These random variables show a behavior that can be considered intermediate between the classical strong law and the Erdös-Rényi law. We further show that the difference from the classical behavior is due to the influence of extreme terms.

On some conditions for the almost everywhere convergence of a class of integrable functions

R. Duncan, D. Szynal (1984)

Colloquium Mathematicae

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Generalized Random Processes on the Zemanian Space a

Z. Lozanov-Crvenković, Stevan Pilipović (1989)

Publications de l'Institut Mathématique

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Further study on complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated random variables

Haiwu Huang, Hanjun Zhang, Qingxia Zhang, Jiangyan Peng (2015)

Kybernetika

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In this paper, the authors further studied the complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated (AANA) random variables with non-identical distribution under some mild moment conditions. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of AANA random variables is obtained. The results not only generalize the corresponding ones of Wang et al. [19], but also partially improve the corresponding...

Convergence of weighted sums of independent random variables and an extension to Banach space-valued random variables.

Padgett, W.J., Taylor, R.L. (1979)

International Journal of Mathematics and Mathematical Sciences

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Exact laws for sums of ratios of order statistics from the Pareto distribution

André Adler (2006)

Open Mathematics

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Consider independent and identically distributed random variables {X nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X n(i) ≤ X n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables R ij = X n(j)/X n(i).

Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients

Igor D. Chueshov, Pierre-A. Vuillermot (1998)

Annales de l'I.H.P. Analyse non linéaire

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