Moment convergence rates in the law of the logarithm for dependent sequences

Let {Xn; n >= 1} be a strictly stationary sequence of negaively associated random variables with mean zero and finite variance. Set S-n = Sigma(n)(k=1) X-k, M-n = max(k <= n) vertical bar S-k vertical bar, n >= 1. Suppose sigma(2) = EX12 + 2 Sigma(k=2EX1Xk)-E-infinity (0 < sigma < infinity). In this paper, the convergence rates of a kind of weighted infinite series of E{M-n-sigma epsilon root n log n} + and E{vertical bar S-n vertical bar - sigma epsilon root n log n} + as epsilon SE arrow 0 and E{sigma epsilon root pi(2)n/8 log n - M-n)(+) as epsilon NE arrow infinity are obtained.