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.
Keywords
Cite
@article{arxiv.1307.2419,
title = {Limit theorems for weighted functionals of cyclical long-range dependent random fields},
author = {Andriy Olenko},
journal= {arXiv preprint arXiv:1307.2419},
year = {2013}
}
Comments
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]