A universal result in almost sure central limit theorem for products of sums of partial sums under mixing sequence

摘要

Let {Xn, n >= 1} be a strictly stationary f-mixing sequence of positive random variables with EX1 = mu > 0, and VarX1 = s2 < 8. Denote Sn = mu ni = 1 Xi, Tn = mu ni = 1 Si and. = s/ mu the coefficient of variation. Under some suitable conditions, the author shows that a universal version of almost sure central limit theorem for products of sums of partial sums holds under the assumptions that the mixing coefficients satisfy mu 8 n= 1 f1/ 2( n) < 8, moreover we no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences.