Limit theorems for weighted functionals of cyclical long-range dependent random fields

Abstract

The paper investigates isotropic random fields for which the spectral density is unbounded at some frequencies. Limit theorems for weighted functionals of these random fields are established. It is shown that for a wide class of functionals, which includes the Donsker scheme, the limit is not affected by singularities at non-zero frequencies. For general schemes, in contrast to the Donsker line, we demonstrate that the singularities at non-zero frequencies play a role even for linear functionals.

19 pages, 2 figures. This is an Author's Accepted Manuscript of an article in the Stochastic Analysis and Applications, Vol. 31, No. 2. (2013), 199--213. [copyright Taylor \& Francis], available online at: http://www.tandfonline.com/ [DOI:10.1080/07362994.2013.741410]

References in corpus (2)

• Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra
• The V/S test of long-range dependence in random fields

Cited by in corpus (5)

• On the rate of convergence to Rosenblatt-type distribution
• Asymptotic behaviour of functionals of cyclical long-range dependent random fields
• Asymptotic Behaviour of Discretised Functionals of Long-Range Dependent Functional Data
• Estimation of seasonal long-memory parameters
• Multiscaling limit theorems for stochastic FPDE with cyclic long-range dependence