View More View Less
  • 1 Faculty of Informatics, University of Debrecen P.O. Box 12, 4010 Debrecen, Hungary
  • | 2 Department of Math. Stat. And Probability, Chebotarev Inst. Of Mathematics and Mechanics, Kazan State University Universitetskaya 17, 420008 Kazan, Russia
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

Almost sure limit theorems are presented for random allocations. A general almost sure limit theorem is proved for arrays of random variables. It is applied to obtain almost sure versions of the central limit theorem for the number of empty boxes when the parameters are in the central domain. Almost sure versions of the Poisson limit theorem in the left domain are also proved.

  • Berkes, I., CÁki, E., Csörgö, S. and Megyesi, Z., Almost sure limit theorems for sums and maxima from the domain of geometrical partial attraction of semistable laws, in: Limit theorems in probability and statistics, Vol. I, 133-157, János Bolyai Math. Soc. (Budapest, 2002). MR2004c:60080

    Limit theorems in probability and statistics , () 133 -157.

  • Dudley, R. M., Real Analysis and Probability, Wadsworth & Brooks/Cole, Pacific Grove, CA (1989). MR91q:60001

    Real Analysis and Probability , ().

  • Fazekas, I. and Chuprunov, A., Almost sure limit theorems for the Pearson statistic (in Russian), Teor. Veroyatnost. i Primenen.48(1) (2003), 162-169. MR2004h:60040

    'Almost sure limit theorems for the Pearson statistic (in Russian) ' () 48 Teor. Veroyatnost. i Primenen. : 162 -169.

    • Search Google Scholar
  • Fazekas, I. and Rychlik, Z., Almost sure functional limit theorems, Ann. Univ. Mariae Curie-Sklodowska, LublinLVI(1) (2002), 1-18. MR2004d:60077

    'Almost sure functional limit theorems ' () LVI Ann. Univ. Mariae Curie-Sklodowska, Lublin : 1 -18.

    • Search Google Scholar
  • Fazekas, I. and Rychlik, Z., Almost sure central limit theorems for random fields, Math. Nachr.259 (2003), 12-18. MR2004i:60035

    'Almost sure central limit theorems for random fields ' () 259 Math. Nachr. : 12 -18.

  • Gut, A., Strong laws for independent identically distributed random variables indexed by a sector, Ann. Probab.11(3) (1983), 569-577. MR85a:60036

    'Strong laws for independent identically distributed random variables indexed by a sector ' () 11 Ann. Probab. : 569 -577.

    • Search Google Scholar
  • Kolchin, V. F., Sevast'Yanov, B. A. and Chistyakov, V. P., Random allocations, V. H. Winston & Sons, Washington D.C. (1978). MR57#10758b

    Random allocations , ().

  • Major, P., Almost sure functional limit theorems, Part I. The general case, Studia Sci. Math. Hungar.34 (1998), 273-304. MR99h:60074

    'Almost sure functional limit theorems, Part I. The general case ' () 34 Studia Sci. Math. Hungar. : 273 -304.

    • Search Google Scholar
  • Móri, T. and Székely, B., Almost sure convergence of weighted partial sums, Acta Math. Hungar.99(4) (2003), 285-303. MR2004a:60071

    'Almost sure convergence of weighted partial sums ' () 99 Acta Math. Hungar. : 285 -303.

  • RÉNYI, A., Three new proofs and generalization of a theorem of Irving Weiss, Magy. Tud. Akad. Mat. Kutató Int. Közl.7(1-2) (1962), 203-214. MR26#5603

    'Three new proofs and generalization of a theorem of Irving Weiss ' () 7 Magy. Tud. Akad. Mat. Kutató Int. Közl. : 1 -2.

    • Search Google Scholar
  • Weiss, I., Limiting distributions in some occupancy problems, Ann. Math. Statist.29(3), 878-884 (1958). MR20#4881

    'Limiting distributions in some occupancy problems ' () 29 Ann. Math. Statist. : 878 -884.

    • Search Google Scholar
  • Brkes, I., Results and problems related to the pointwise central limit theorem, in:Szyszkowicz, B. (Ed.) Asymptotic results in probability and statistics. Elsevier, Amsterdam (1998), 59-96. MR99k:60080

    Asymptotic results in probability and statistics. , () 59 -96.

  • Berkes, I. and Csáki, E., A universal result in almost sure central limit theory, Stock. Proc. Appl.94(1) (2001), 105-134. MR2002j:60033

    'A universal result in almost sure central limit theory ' () 94 Stock. Proc. Appl. : 105 -134.

    • Search Google Scholar
  • Berkes, I., Csaki, E. and Csörgö, S., Almost sure limit theorems for the St. Petersburg game, Satist. Probab. Lett.45 (1999), 23-30. MR2001f:60033

    'Almost sure limit theorems for the St. Petersburg game ' () 45 Satist. Probab. Lett. : 23 -30.

    • Search Google Scholar
  • BÉKÉSSY, A., On classical occupancy problems. I, Magy. Tud. Akad. Mat. Kutató Int. Közl.8(1-2) (1963), 59-71. MR29#2826

    'On classical occupancy problems. I ' () 8 Magy. Tud. Akad. Mat. Kutató Int. Közl. : 1 -2.

    • Search Google Scholar