Authors:
István Berkes Alfréd Rényi Institute of Mathematics, Budapest, Hungary

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Endre Csáki Alfréd Rényi Institute of Mathematics, Budapest, Hungary

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Generalizing results of Schatte [11] and Atlagh and Weber [2], in this paper we give conditions for a sequence of random variables to satisfy the almost sure central limit theorem along a given sequence of integers.

  • [1]

    Atlagh, M. Théorème central limite presque sûr et loi du logarithme itéré pour des sommes de variables aléatoires indépendantes. C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), 929933.

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  • [2]

    Atlagh, M., and Weber, M. Un théorème central limite presque sûr relatif à des sous-suites. C. R. Acad. Sci. Paris Sér. I 315 (1992), 203206.

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  • [3]

    Berkes, I., and Dehling, H. Some limit theorems in log density, Ann. Probab. 21 (1993), 16401670.

  • [4]

    Bingham, N. H., and Rogers, L. C. G. Summability methods and almost sure convergence. In: Bellow, A., Jones, R., editors, Almost Everywhere Convergence II, Academic Press, New York, 1991, pages 6983.

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    • Export Citation
  • [5]

    Chandrasekharan, K., and Minakshisundaram, S. Typical Means. Oxford University Press, Oxford, 1952.

  • [6]

    Dudley, R. M. Probabilities and metrics. Lecture Notes Series 45, Aarhus Universitet, 1976.

  • [7]

    Ibragimov, I. A., and Lifshits, M. A. On limit theorems of “almost sure” type. (Russian) Teor. Veroyatnost. i Primenen. 44 (1999), 328350; translation in Theory Probab. Appl. 44 (2000), 254272.

    • Search Google Scholar
    • Export Citation
  • [8]

    Lifshits, M. The almost sure limit theorem for sums of random vectors, J. Math. Sciences 109 (2002), 21662178.

  • [9]

    Major, P. Almost sure functional limit theorems. I. The general case. Studia Sci. Math. Hungar. 34 (1998), 273304.

  • [10]

    Major, P. Almost sure functional limit theorems. II. The case of independent random variables. Studia Sci. Math. Hungar. 36 (2000), 231273.

    • Search Google Scholar
    • Export Citation
  • [11]

    Schatte, P. On strong versions of the central limit theorem. Math. Nachr. 137 (1988), 249256.

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Editor in Chief: László TÓTH, University of Pécs, Pécs, Hungary

Honorary Editors in Chief:

  • János PINTZ, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • † Ferenc SCHIPP, Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary
  • Sándor SZABÓ, University of Pécs, Pécs, Hungary
     

Deputy Editors in Chief:

  • Erhard AICHINGER, JKU Linz, Linz, Austria
  • Ferenc HARTUNG, University of Pannonia, Veszprém, Hungary
  • Ferenc WEISZ, Eötvös Loránd University, Budapest, Hungary

Editorial Board

  • Attila BÉRCZES, University of Debrecen, Debrecen, Hungary
  • István BERKES, Rényi Institute of Mathematics, Budapest, Hungary
  • Károly BEZDEK, University of Calgary, Calgary, Canada
  • György DÓSA, University of Pannonia, Veszprém, Hungary
  • Balázs KIRÁLY – Managing Editor, University of Pécs, Pécs, Hungary
  • Vedran KRCADINAC, University of Zagreb, Zagreb, Croatia 
  • Željka MILIN ŠIPUŠ, University of Zagreb, Zagreb, Croatia
  • Gábor NYUL, University of Debrecen, Debrecen, Hungary
  • Margit PAP, University of Pécs, Pécs, Hungary
  • István PINK, University of Debrecen, Debrecen, Hungary
  • Mihály PITUK, University of Pannonia, Veszprém, Hungary
  • Lukas SPIEGELHOFER, Montanuniversität Leoben, Leoben, Austria
  • Andrea ŠVOB, University of Rijeka, Rijeka, Croatia
  • Csaba SZÁNTÓ, Babeş-Bolyai University, Cluj-Napoca, Romania
  • Jörg THUSWALDNER, Montanuniversität Leoben, Leoben, Austria
  • Zsolt TUZA, University of Pannonia, Veszprém, Hungary

Advisory Board

  • Szilárd RÉVÉSZ – Chair, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Gabriella BÖHM
  • György GÁT, University of Debrecen, Debrecen, Hungary

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
  • Zentralblatt
  • DOAJ

Publication Model Gold Open Access
Online only
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Subscription Information Gold Open Access

Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Volumes
per Year
1
Issues
per Year
2
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)