Strong Approximation for Moving Average Processes Under Dependence Assumptions

Let {Xt ≥ 1} be a moving average process defined by where {akk ≥ 0} is a sequence of real numbers and {ɛt, – ∞ < t < ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {akk ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, 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.