{
  "id": "1802.06577",
  "version": "v1",
  "published": "2018-02-19T10:13:01.000Z",
  "updated": "2018-02-19T10:13:01.000Z",
  "title": "The exact asymptotics for hitting probability of a remote orthant by a multivariate Lévy process: the Cramér case",
  "authors": [
    "Konstantin Borovkov",
    "Zbigniew Palmowski"
  ],
  "comment": "7 pages, 0 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "For a multivariate L\\'evy process satisfying the Cram\\'er moment condition and having a drift vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant that is being translated to infinity along a fixed vector with positive components. This problem is motivated by the multivariate ruin problem introduced in F. Avram et al. (2008) in the two-dimensional case. Our solution relies on the analysis from Y. Pan and K. Borovkov (2017) for multivariate random walks and an appropriate time discretization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-19T10:13:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G51"
    ],
    "keywords": [
      "multivariate lévy process",
      "exact asymptotics",
      "remote orthant",
      "cramér case",
      "hitting probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}