On a random functional central limit theorem for a stationary multivariate linear process generated by linearly positive quadrant dependent random vectors

For a stationary multivariate linear process of the form X-t = Sigma(j=0)(infinity) A(j)Z(t-j), where {Z(t) : t = 0, +/-1, +/-2,...} is a sequence of stationary linearly positive quadrant dependent m-dimensional random vectors with mean O and positive definite covariance matrix Gamma, we prove a random functional central limit theorem.