Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 56: Issue 2
Almost sure central limit theorems for weighted dependent sequences
Author: Khurelbaatar Gonchigdanzan 1
View More View Less
  • 1 University of Wisconsin - Stevens Point, Stevens Point, WI 54481, USA
DOI:
https://doi.org/10.1556/012.2019.56.2.1426
Page Count:
145–153
Publication Date:
01 Jun 2019
Online Publication Date:
Jun 2019
Article Category:
Research Article
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00
Purchase Online Subscription

  • 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 ≦ k ≦ n, 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.

limn→∞1log n∑k=1n1kI(∑i=1kwkiXi≦x)=12π∫−∞xe−12t2dt  a.s..

  • [1]

    Berkes, I. and Csáki, E., (2001), A universal result in almost sure central limit theory. Stoch. Proc. Appl. 94 (1), 105–134.
  • [2]

    Berkes, I. and Dehling, H., Some limit theorems in log density, Ann. Probab., 21 (3) (1993), 1640–1670.
  • [3]

    Brosamler, G. A., An almost everywhere central limit theorem, Math. Proc. Camb. Phil. Soc., 104 (1988), 561–574.
  • [4]

    Gonchigdanzan, K., Almost sure central limit theorems for strongly mixing and associated random variables, Inter. J. of Math., 29 (3) (2001), 125–131.

    • Search Google Scholar
    • Export Citation
  • [5]

    Lehmann, E. L., Some concepts of dependence, Ann. Math. Statist., 37 (5) (1966), 1137–1153.
  • [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), 131–136.

    • Search Google Scholar
    • Export Citation
  • [7]

    Peligrad, M. and Utev, S., Central limit theorem for linear processes, Ann. Probab. 25 (1) (1997), 443–456.
  • [8]

    Rio, E., Covariance inequalities for strongly mixing processes, Ann. Inst. H. Poincaré Probab. Stat., 29 (1993), 587–597.
  • [9]

    Schatte, P., On strong versions of the central limit theorem, Math. Nachr. 137 (1988), 249–256.
Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896
Keywords:
Almost sure central limit theorem; logarithmic average; weighted partial sum; dependent variables

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Sep 2020 4 0 0
Oct 2020 8 0 0
Nov 2020 7 0 0
Dec 2020 4 0 0
Jan 2021 18 1 1
Feb 2021 19 0 0
Mar 2021 0 0 0