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On almost sure local and global central limit theorems
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  • Published: September 1993

On almost sure local and global central limit theorems

  • E. Csáki1,
  • A. Földes2 &
  • P. Révész3 

Probability Theory and Related Fields volume 97, pages 321–337 (1993)Cite this article

  • 152 Accesses

  • 21 Citations

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Summary

LetS 1,S 2,... be a sequence of sums of i.i.d. random variables. The properties of the logarithmic average

$$\frac{1}{{\log n}}\sum\limits_{k = 1}^n {\frac{{I\{ a_k \leqq S_k< b_k \} }}{{kP(a_k \leqq S_k< b_k )}}}$$

will be studied under some conditions.

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Author information

Authors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, H-1364, Budapest, Hungary

    E. Csáki

  2. City University of New York, 130 Stuyvesant Place, 10301, Staten Island, NY, USA

    A. Földes

  3. Institut für Statistik und Wahrscheinlichkeitstheorie, Technische Universität Wien, Wiedner Hauptstrasse 8-10/107, A-1040, Wien, Austria

    P. Révész

Authors
  1. E. Csáki
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  2. A. Földes
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  3. P. Révész
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Additional information

Dedicated to Paul Erdős on the occasion of his 80th birthday

Research supported by Hungarian National Foundation for Scientific Research, Grant No. 1905 and CUNY Research Grant No. 662349

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Cite this article

Csáki, E., Földes, A. & Révész, P. On almost sure local and global central limit theorems. Probab. Th. Rel. Fields 97, 321–337 (1993). https://doi.org/10.1007/BF01195069

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  • Received: 11 May 1992

  • Revised: 22 April 1993

  • Issue Date: September 1993

  • DOI: https://doi.org/10.1007/BF01195069

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Mathematics Subject Classification (1991)

  • 60F15
  • 60F05
  • 60J15
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