A general law of precise asymptotics for products of sums under dependence

Let .ub;X n , n . 1.ub; be a strictly stationary LNQD (LPQD) sequence of positive random variables with EX 1 = µ > 0, and VarX 1 = . 2 < .. Denote by S n = . ni=1 X i and . = ./µ the coefficients of variation. In this paper, under some suitable conditions, we show that a general law of precise asymptotics for products of sums holds. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in the study of complete convergence.