Inequalities and limit theorems for random allocations

Istvan Fazekas, Alexey Chuprunov, Jozsef Turi

Abstract


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.

Keywords


Random allocation; moment inequality; merge theorem; almost sure limit theorem

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References


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DOI: http://dx.doi.org/10.2478/v10062-011-0006-5
Date of publication: 2016-07-25 18:17:32
Date of submission: 2016-07-25 17:45:59


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