Displaying similar documents to “Inequalities and limit theorems for random allocations”

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.

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.

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.