ABSTRACT
The covariance functional of X(·) is given byr(h1,h2) = IRn –{0} IRn –{0} h1( )h2( ')dF( , ') + (A M h1(0), M h2(0))15
with A a positive definite matrix. As noted before, the conditions upon g are satisfied when g(t, ) = ei ·t,
in which case the previous representation specializes to:
h( )dZY( ) + (–1)M ( , Mh(0)) where ZY(·) is the spectral measure associated with its strongly harmoniz able Mth order partial derivative field Y(·) = X(m1, m2, . . ., mn)(h)(·) and h is the Fourier transform of h and ZY, a second-order random vector and M as defined above.
