The complete convergence of linear process generated by ρ−-mixing sequence

Let {Y_i;-∞ <; i <; ∞} be indentically distributed random variables sequence, {α_i;-∞ <; i <; ∞} be an absolutely summable sequence of real numbers. Since the concept of complete convergence was proposed, many people have been paying attention to it´s limit properties. Because ρ^- -mixing sequence is a class of mixing sequence with wide applications, such as in finance, electron, hydrology, the corresponding limit properties are worth studying. In this paper, we discuss the complete convergence of linear process generated by ρ^--mixing sequence with slowly varying function by moment inequality.