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2011 | 65 | 1 |
Tytuł artykułu

Inequalities and limit theorems for random allocations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
65
Numer
1
Opis fizyczny
Daty
wydano
2011
online
2016-07-25
Twórcy
Bibliografia
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2011_65_1_69-85
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