An almost sure central limit theorem of products of partial sums for [rho]^sup -^-mixing sequences

Let {X ^sub n^, n >= 1} be a strictly stationary [rho] ^sup -^-mixing sequence of positive random variables with EX ^sub 1^ = [mu] > 0 and Var(X ^sub 1^) = [sigma] ^sup 2^ < ∞. Denote [InlineEquation not available: see fulltext.] and [InlineEquation not available: see fulltext.] the coefficient of variation. Under suitable conditions, by the central limit theorem of weighted sums and the moment inequality we show that [Equation not available: see fulltext.] where [InlineEquation not available: see fulltext.] with [InlineEquation not available: see fulltext.] is the distribution function of the random variable [InlineEquation not available: see fulltext.], and [InlineEquation not available: see fulltext.] is a standard normal random variable. MR(2000) Subject Classification: 60F15.[PUBLICATION ABSTRACT]