International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 19, Pages 3195-3198
doi:10.1155/IJMMS.2005.3195

A note on the strong law of large numbers for associated sequences

Abstract

We prove that the sequence {bn−1∑i=1n(Xi−EXi)}n≥1 converges a.e. to zero if {Xn,n≥1} is anassociated sequence of random variables with ∑n=1∞bkn−2Var(∑i=kn−1+1knXi)<∞ where {bn,n≥1} is a positive nondecreasing sequence and {kn,n≥1} is a strictly increasing sequence, both tending to infinity as n tends to infinity and 0<a=infn≥1bknbkn+1−1≤supn≥1bknbkn+1−1=c<1.