Asymptotics of maxima and sums for a type of strongly dependent isotropic Gaussian random fields

For a type of strongly dependent isotropic Gaussian random fields introduced by Mittal (1976 Mittal, Y. 1976. A class of isotropic covariances functions. Pacific Journal of Mathematics 64:517–38.Crossref], Web of Science ®] , Google Scholar]), the joint limiting distribution of the maximum and the sum for the Gaussian random fields is derived. The asymptotic relation between the maximum and sum of the continuous time strongly dependent isotropic Gaussian random fields and the maximum and sum of this fields sampled at discrete time points is also obtained.