ArticleOriginal scientific text
Title
Inequalities and limit theorems for random allocations
Authors , ,
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
Bibliography
- 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.
- Bekessy, A., On classical occupancy problems. I, Magy. Tud. Akad. Mat. Kutató Int. Kozl. 8 (1-2) (1963), 59-71.
- 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.
- Berkes, I., Csaki, E., A universal result in almost sure central limit theory, Stoch. Proc. Appl. 94(1) (2001), 105-134.
- Chuprunov, A., Fazekas, I., Inequalities and strong laws of large numbers for random allocations, Acta Math. Hungar. 109, no. 1-2 (2005), 163-182.
- Fazekas, I., Chuprunov, A., Almost sure limit theorems for random allocations, Studia Sci. Math. Hungar. 42, no. 2 (2005), 173-194.
- 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.
- Fazekas, I., Rychlik, Z., Almost sure functional limit theorems, Ann. Univ. Mariae Curie-Skłodowska Sect. A 56(1) (2002), 1-18.
- Fazekas, I., Rychlik, Z., Almost sure central limit theorems for random fields, Math. Nachr. 259 (2003), 12-18.
- Hormann, S., An extension of almost sure central limit theory, Statist. Probab. Lett. 76, no. 2 (2006), 191-202.
- 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.
- Kolchin, V. F., Sevast’yanov, B. A. and Chistyakov, V. P., Random Allocations, V. H. Winston & Sons, Washington D. C., 1978.
- Matuła, P., On almost sure limit theorems for positively dependent random variables, Statist. Probab. Lett. 74, no. 1 (2005), 59-66.
- 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.
- Orzóg, M., Rychlik, Z., On the random functional central limit theorems with almost sure convergence, Probab. Math. Statist. 27, no. 1 (2007), 125-138.
- Weiss, I., Limiting distributions in some occupancy problems, Ann. Math. Statist. 29(3) (1958), 878-884.
Main language of publication
English
Published
2011
Published online
2016-07-25
Exact and natural sciences