{
  "id": "1307.3349",
  "version": "v1",
  "published": "2013-07-12T07:07:28.000Z",
  "updated": "2013-07-12T07:07:28.000Z",
  "title": "Asymptotic behaviour of functionals of cyclical long-range dependent random fields",
  "authors": [
    "Boris Klykavka",
    "Andriy Olenko",
    "Matthew Vicendese"
  ],
  "comment": "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",
  "doi": "10.1007/s10958-012-1047-1",
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-12T07:07:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G60",
      "60F17"
    ],
    "keywords": [
      "cyclical long-range dependent random fields",
      "functionals",
      "regular varying asymptotic behaviour",
      "cyclical long-range dependent fields",
      "weight functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.3349K"
    }
  }
}