Inequalities and limit theorems for random allocations

Istvan Fazekas; Alexey Chuprunov; Jozsef Turi

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2011)

  • Volume: 65, Issue: 1
  • ISSN: 0365-1029

Abstract

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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.

How to cite

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Istvan Fazekas, Alexey Chuprunov, and Jozsef Turi. "Inequalities and limit theorems for random allocations." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 65.1 (2011): null. <http://eudml.org/doc/289835>.

@article{IstvanFazekas2011,
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.},
author = {Istvan Fazekas, Alexey Chuprunov, Jozsef Turi},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Random allocation; moment inequality; merge theorem; almost sure limit theorem},
language = {eng},
number = {1},
pages = {null},
title = {Inequalities and limit theorems for random allocations},
url = {http://eudml.org/doc/289835},
volume = {65},
year = {2011},
}

TY - JOUR
AU - Istvan Fazekas
AU - Alexey Chuprunov
AU - Jozsef Turi
TI - Inequalities and limit theorems for random allocations
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2011
VL - 65
IS - 1
SP - null
AB - 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.
LA - eng
KW - Random allocation; moment inequality; merge theorem; almost sure limit theorem
UR - http://eudml.org/doc/289835
ER -

References

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  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. 

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