ABSTRACT
For a positive integer d, let :!!'" be the lattice of all points in ~" having integer coordinates, and for each n = (n 1, ..• , nd) in ;ld, let Xn be a realvalued r.v. Thus, what we are dealing with here is a random field {Xn, n E ::r"} whose elements take values in ~. The basic assumption on this random field is that it consists of either positively or negatively associated r.v.'s which have finite second moment and are covariance invariant; that is, for any u, v in ::z", Cov(Xu, X,) = C(u-v) for some C: :zd--> R In particular, C(O) = 0'2(X0 ) will be denoted by 0'2, and, by centering the X0 's at their expectations, it will be assumed that Iff X"= 0, n E 2".
