Geodesic
Inequalities and limit theorems for random allocations
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 1.

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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.
Keywords: Random allocation, moment inequality, merge theorem, almost sure limit theorem 
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Fazekas, Istvan; Chuprunov, Alexey; Turi, Jozsef. Inequalities and limit theorems for random allocations. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 1. http://geodesic.mathdoc.fr/item/AUM_2011_65_1_a2/

[1] Becker-Kern, P., An almost sure limit theorem for mixtures of domains in random allocation, Studia Sci. Math. Hungar. 44, no. 3 (2007), 331-354.

[2] Bekessy, A., On classical occupancy problems. I, Magy. Tud. Akad. Mat. Kutató Int. Kozl. 8 (1-2) (1963), 59-71.

[3] Berkes, I., Results and problems related to the pointwise central limit theorem, Szyszkowicz, B., (Ed.), Asymptotic Results in Probability and Statistics, Elsevier, Amsterdam, 1998, 59-96.

[4] Berkes, I., Csaki, E., A universal result in almost sure central limit theory, Stoch. Proc. Appl. 94(1) (2001), 105-134.

[5] Chuprunov, A., Fazekas, I., Inequalities and strong laws of large numbers for random allocations, Acta Math. Hungar. 109, no. 1-2 (2005), 163-182.

[6] Fazekas, I., Chuprunov, A., Almost sure limit theorems for random allocations, Studia Sci. Math. Hungar. 42, no. 2 (2005), 173-194.

[7] Fazekas, I., Chuprunov, A., An almost sure functional limit theorem for the domain of geometric partial attraction of semistable laws, J. Theoret. Probab. 20, no. 2 (2007), 339-353.

[8] Fazekas, I., Rychlik, Z., Almost sure functional limit theorems, Ann. Univ. Mariae Curie-Skłodowska Sect. A 56(1) (2002), 1-18.

[9] Fazekas, I., Rychlik, Z., Almost sure central limit theorems for random fields, Math. Nachr. 259 (2003), 12-18.

[10] Hormann, S., An extension of almost sure central limit theory, Statist. Probab. Lett. 76, no. 2 (2006), 191-202.

[11] Kolchin, A. V., Limit theorems for a generalized allocation scheme, Diskret. Mat. 15, no. 4 (2003), 148-157 (Russian); English translation in Discrete Math. Appl. 13, no. 6 (2003), 627-636.

[12] Kolchin, V. F., Sevast’yanov, B. A. and Chistyakov, V. P., Random Allocations, V. H. Winston Sons, Washington D. C., 1978.

[13] Matuła, P., On almost sure limit theorems for positively dependent random variables, Statist. Probab. Lett. 74, no. 1 (2005), 59-66.

[14] Renyi, A., Three new proofs and generalization of a theorem of Irving Weiss, Magy. Tud. Akad. Mat. Kutató Int. K¨ozl. 7(1-2) (1962), 203-214.

[15] Orzóg, M., Rychlik, Z., On the random functional central limit theorems with almost sure convergence, Probab. Math. Statist. 27, no. 1 (2007), 125-138.

[16] Weiss, I., Limiting distributions in some occupancy problems, Ann. Math. Statist. 29(3) (1958), 878-884.