Abstract. Long-range dependent random fields with spectral densities which are unbounded at some frequencies are investigated. We demonstrate new examples of covariance functions which do not exhibit regular varying asymptotic behaviour at infinity. However, variances of averaged functionals of these fields are regularly varying. Limit theorems for weighted functionals of cyclical long-range dependent fields are obtained. The order of normalizing constants and relations between the weight functions and singularities in non-degenerative asymptotics are discussed.MSC 2010. 60G60, 60F17
Abstract. 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.
We continue the studies of weight functions in Tauberian theorems for random fields. We obtain the rate of convergence of function series in the representation of a weight function and prove a recurrence relation for weight functions in spaces of various dimensions.
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