Displaying similar documents to “On some conditions for the almost everywhere convergence of a class of integrable functions”

One sided strong laws for random variables with infinite mean

André Adler (2017)

Open Mathematics

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This paper establishes conditions that secure the almost sure upper and lower bounds for a particular normalized weighted sum of independent nonnegative random variables. These random variables do not possess a finite first moment so these results are not typical. These mild conditions allow us to show that the almost sure upper limit is infinity while the almost sure lower bound is one.

Inequalities and limit theorems for random allocations

István Fazekas, Alexey Chuprunov, József Túri (2011)

Annales UMCS, 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

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.

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 the convergence of moments in the CLT for triangular arrays with an application to random polynomials

Christophe Cuny, Michel Weber (2006)

Colloquium Mathematicae

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We give a proof of convergence of moments in the Central Limit Theorem (under the Lyapunov-Lindeberg condition) for triangular arrays, yielding a new estimate of the speed of convergence expressed in terms of νth moments. We also give an application to the convergence in the mean of the pth moments of certain random trigonometric polynomials built from triangular arrays of independent random variables, thereby extending some recent work of Borwein and Lockhart.

Complete convergence of weighted sums for arrays of rowwise ϕ -mixing random variables

Xinghui Wang, Xiaoqin Li, Shuhe Hu (2014)

Applications of Mathematics

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In this paper, we establish the complete convergence and complete moment convergence of weighted sums for arrays of rowwise ϕ -mixing random variables, and the Baum-Katz-type result for arrays of rowwise ϕ -mixing random variables. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of ϕ -mixing random variables is obtained. We extend and complement the corresponding results of X. J. Wang, S. H. Hu (2012).