{
  "id": "2108.09225",
  "version": "v1",
  "published": "2021-08-20T15:30:04.000Z",
  "updated": "2021-08-20T15:30:04.000Z",
  "title": "Extremes of Gaussian random fields with non-additive dependence structure",
  "authors": [
    "Long Bai",
    "Krzysztof Debicki",
    "Peng Liu"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We derive exact asymptotics of $$\\mathbb{P}\\left(\\sup_{t\\in \\mathcal{A}}X(t)>u\\right), ~\\text{as}~ u\\to\\infty,$$ for a centered Gaussian field $X(t),~t\\in \\mathcal{A}\\subset\\mathbb{R}^n$, $n>1$ with continuous sample paths a.s. and general dependence structure, for which $\\arg \\max_{t\\in {\\mathcal{A}}} Var(X(t))$ is a Jordan set with finite and positive Lebesque measure of dimension $k\\leq n$. Our findings are applied to deriving the asymptotics of tail probabilities related to performance tables and dependent chi processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-20T15:30:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G70"
    ],
    "keywords": [
      "gaussian random fields",
      "non-additive dependence structure",
      "general dependence structure",
      "dependent chi processes",
      "centered gaussian field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}