ALMOST SURE CENTRAL LIMIT THEOREMS FOR WEIGHTED DEPENDENT SEQUENCES

Let {X-n : n >= 1} be a sequence of dependent random variables and let {w(nk) : 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. lim (n ->infinity) 1/log n Sigma(n)(k=1) 1/k I (Sigma(k)(i=1) w(ki)X(i) <= x) = 1/root 2 pi integral(x)(-infinity) e(-1/2t2) dt a.s..