A limit theorem for random fields with a singularity in the spectrum
Andriy Ya. Olenko, B. M. Klykavka · Theory of Probability and Mathematical Statistics · 2010
Homogeneous isotropic random fields with singularities in spectra at nonzero frequencies are studied. This class of fields generalizes the case of random fields with long range dependence where the spectrum has a singularity at the origin. We obtain a limit theorem for integral weight functionals of the field. We also discuss the difference between this class and the long range dependence.