International Journal of Mathematics and Mathematical Sciences 
Volume 29 (2002), Issue 3, Pages 125-131
doi:10.1155/S0161171202011626

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

Abstract

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)−1−δ). We also show that ASCLT holds for an associated sequence of random variables without a stationarity assumption.