Orsingher, Enzo et Bassan, Bruno, On the comparison of the distribution of the supremum of random fields represented by stochastic integrals, Advances in applied probability , 21(4), 1989, pp. 770-780
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 = .2, between fields with different response functions.