Boris Klykavka, Andriy Olenko, Matthew Vicendese
Published 2013-07-12Version 1
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.
Comments: 18 pages, 6 figures. This is an Author's Accepted Manuscript of an article published in the Ukrainian Mathematical Bulletin, Vol.9, No. 2. (2012), 191--208. and republished by Journal of Mathematical Sciences. Vol.187, No. 1. (2012), 35--48. The final publication is available at link.springer.com
Journal: Ukrainian Mathematical Bulletin, Vol.9, No. 2. (2012), 191--208; Journal of Mathematical Sciences. Vol.187, No. 1. (2012), 35--48
Limit theorems for weighted functionals of cyclical long-range dependent random fields
A Note on Homogenization of Dynamics and Functionals of Generalized Langevin Systems
Non-central limit theorems for functionals of random fields on hypersurfaces
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