Joint behavior of point processes of clusters and partial sums for stationary bivariate Gaussian triangular arrays

Point process of clusters for a stationary Gaussian random field on a lattice

“…The asymptotic distribution of the maximum of a Gaussian random field was established in which the spatial domain is rescaled. Recently, [12] established asymptotic behaviors of point processes of clusters for stationary bivariate Gaussian triangular arrays. However, to the best of our knowledge, there is not much research on the point process of a Gaussian random field on a lattice, because the theoretical development of multivariate extreme value theory is far behind its univariate counterpart.…”

“…Motivated by [11,12], we consider asymptotic behaviors of the point process of clusters for a Gaussian random field {X n,ij , 0 i, j n} on a lattice. Similar to the definition of N n (B), the point process of clusters formed by {X n,ij , 0 i, j n} is defined by…”