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

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

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

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    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.

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

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

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

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  • [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)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • György DÓSA (University of Pannonia, Veszprém)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Margit PAP (University of Pécs)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM (Akadémiai Kiadó, Budapest)
  • György GÁT (University of Debrecen)

University of Pécs,
Faculty of Sciences,
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Department of Mathematics
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ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
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Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Volumes
per Year
1
Issues
per Year
2
Founder Akadémiai Kiadó
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Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
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ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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