Abstract: Let {X_t,t ≥ 1} be a moving average process defined by
$X_{t}=\sum\limits_{k=0}^{\infty}a_{k}\xi_{t-k}$, where {a_k,k ≥ 0} is a sequence of real numbers and {ξ_t,-∞ < t<∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {a_k,k ≥ 0} which entail that {X_t,t ≥ 1} is either a long memory process or a linear process, the strong approximation of {X_t,t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.

Key words: Strong approximation, long memory process, linear process, fractional Brownian motion, the law of the iterated logarithm