Gaussian random fields with projective invariance

Abstract

We shall consider the class of Gaussian random fields Xα = {X(A); A ∈ Rn} such that E{X(A) − X(B)} = 0 and E{(X(A) − X(B))2} = |A − B|α (0 < α < 2), where |A − B| denotes the Euclidean distance between two points A and B.