A general result on precise asymptotics for linear processes of positively associated sequences

Let { ε t ; t ∈ Z + } be a strictly stationary sequence of associated random variables with mean zeros, let 0 < Eε 1 2 < ∞ and with 0 < σ 2 < ∞. { a j ; j ∈ Z + } is a sequence of real numbers satisfying . Define a linear process , and . Assume that E |ε 1 | 2+ δ ′ < ∞ for some δ′ > 0 and µ( n ) = O ( n − ρ ) for some ρ > 0. This paper achieves a general law of precise asymptotics for { S n }.