Precise rates in complete moment convergence for ρ-mixing sequences

Let X-1, X-2,... be a strictly stationary sequence of rho-mixing random variables with mean zeros and positive, finite variances, set S-n = X-1 + center dot center dot center dot + X-n. Suppose that lim(n)-> ESn2/n = sigma(2) > 0, Sigma(infinity)(n=1) rho(2/q) (2(n)) < infinity, where q > 2 delta + 2. We prove that, if EX12(log(+) vertical bar X-1 vertical bar)(delta) < infinity for any 0 < delta <= 1, then [GRAPHICS] where N is the standard normal random variable. (c) 2007 Elsevier Inc. All rights reserved.