{
  "id": "1810.09285",
  "version": "v1",
  "published": "2018-10-19T12:29:16.000Z",
  "updated": "2018-10-19T12:29:16.000Z",
  "title": "Non-central limit theorems for functionals of random fields on hypersurfaces",
  "authors": [
    "Andriy Olenko",
    "Volodymyr Vaskovych"
  ],
  "comment": "35 pages. arXiv admin note: text overlap with arXiv:1703.05900",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in $\\mathbb{R}^d$. We obtain the rate of convergence for these functionals. The results extend recent findings for solid figures. We apply the obtained results to the case of sojourn measures and demonstrate different limit situations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-19T12:29:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G60",
      "60F05",
      "60G12"
    ],
    "keywords": [
      "non-central limit theorems",
      "functionals",
      "paper derives non-central asymptotic results",
      "hypersurfaces",
      "homogeneous isotropic gaussian random fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}