In this paper we compare the distribution of the supremum of the Gaussian random fields Z(P) = ∫CpG(P, P′) dW(P′) and U(P) = ∫CpdW(P'), where CP are circles of fixed radius, dW is a white noise field and G are special deterministic response functions.
The results obtained permit us to establish upper bounds for the distribution of the supremum of Z(P) by applying some well-known inequalities on U(P).
The comparison of the suprema is carried out also, when CP = ℝ2, between fields with different response functions.
