International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 3, Pages 125-131

Almost sure central limit theorems for strongly mixing and associated random variables

Khurelbaatar Gonchigdanzan

Department of Mathematical Sciences, University of Cincinnati, Cincinnati 45221-0025, OH, USA

Received 24 January 2001; Revised 9 June 2001

Copyright © 2002 Khurelbaatar Gonchigdanzan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove an almost sure central limit theorem (ASCLT) for strongly mixing sequence of random variables with a slightly slow mixing rate α(n)=O((loglogn)1δ). We also show that ASCLT holds for an associated sequence of random variables without a stationarity assumption.