Precise asymptotics for the linear processes generated by associated random variables in Hilbert spaces

Let {εk,k∈Z} be a strictly stationary associated sequence of random variables taking values in a real separable Hilbert space, and {ak;k∈Z} be a sequence of bounded linear operators. For a linear process Xk=∑i=−∞∞ai(εk−i), the precise probability and moment convergence rates of ∑i=1nXi in some limit theorems are discussed.