View More View Less
  • 1 University of Wisconsin - Stevens Point, Stevens Point, WI 54481, USA
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

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.

    • Search Google Scholar
    • Export Citation
  • [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.

    • Search Google Scholar
    • Export Citation
  • [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.

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE

 

  • Impact Factor (2018): 0.309
  • Mathematics (miscellaneous) SJR Quartile Score (2018): Q3/li>
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • SCOPUS
  • The ISI Alerting Services

 

Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu