Limit theorems for filtered long-range dependent random fields

This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of long-range dependent fields and increasing observation windows is studied. The obtained limit random processes are non-Gaussian. Most known results on this topic give asymptotic processes that always exhibit non-negative auto-correlation structures and have the self-similar parameter (Formula presented.). In this work, we also obtain convergence for the case (Formula presented.) and show how the Hurst parameter H can depend on the shape of the observation windows. Various examples are presented.