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Abstract

Let {Xn: n ≧ 1} be a sequence of dependent random variables and let {wnk: 1 ≦ kn, n ≧ 1} be a triangular array of real numbers. We prove the almost sure version of the CLT proved by Peligrad and Utev [7] for weighted partial sums of mixing and associated sequences of random variables, i.e.
limn1lognk=1n1kI(i=1kwkiXix)=12πxe12t2dta.s..
  • [1]

    Berkes, I. and Csáki, E., (2001), A universal result in almost sure central limit theory. Stoch. Proc. Appl. 94 (1), 105134.

  • [2]

    Berkes, I. and Dehling, H., Some limit theorems in log density, Ann. Probab., 21 (3) (1993), 16401670.

  • [3]

    Brosamler, G. A., An almost everywhere central limit theorem, Math. Proc. Camb. Phil. Soc., 104 (1988), 561574.

  • [4]

    Gonchigdanzan, K., Almost sure central limit theorems for strongly mixing and associated random variables, Inter. J. of Math., 29 (3) (2001), 125131.

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  • [5]

    Lehmann, E. L., Some concepts of dependence, Ann. Math. Statist., 37 (5) (1966), 11371153.

  • [6]

    Peligrad, M. and Shao, Q. M., A note on the almost sure central limit theorem for weakly dependent random variables, Stat. Prob. Letters 22 (2) (1995), 131136.

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  • [7]

    Peligrad, M. and Utev, S., Central limit theorem for linear processes, Ann. Probab. 25 (1) (1997), 443456.

  • [8]

    Rio, E., Covariance inequalities for strongly mixing processes, Ann. Inst. H. Poincaré Probab. Stat., 29 (1993), 587597.

  • [9]

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

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
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2019  
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463
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without
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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation
1966
Publication
Programme
2021 Volume 58
Volumes
per Year
1
Issues
per Year
4
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
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H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
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Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)