Abstract: Let {ε_t;t∈Z^{+} be a strictly stationary sequence of LPQD random variables with mean zeros, let 02₁<∞,with 0<σ2<∞, {_j;; j∈N } is a sequence of real numbers satisfying. Define a linear process X_t. In this article, by means of the weak convergence theorems and moment inequalities, the precise asymptotics of {M_n} and {S_n}is proved for more general weighted functions and boundary functions.}

Key words: linear processes, LPQD sequences, precise asymptotics, partial sum