Equivalence of measures for some class of Gaussian random fields

We consider two Gaussian measures P1 and P2 on (C(G), ) with zero expectations and covariance functions R1(x, y) and R2(x, y) respectively, where R[nu](x, y) is the Green's function of the Dirichlet problem for some uniformly strongly elliptic differential operator A([nu]) of order 2m, m >= [d/2] + 1, on a bounded domain G in d ([nu] = 1, 2). It is shown that if the order of A(2) - A(1) is at most 2m - [d/2] - 1, then P1 and P2 are equivalent, while if the order is greater than 2m - [d/2] - 1, then P1 and P2 are not always equivalent.