{
  "id": "2107.11322",
  "version": "v1",
  "published": "2021-07-23T16:01:44.000Z",
  "updated": "2021-07-23T16:01:44.000Z",
  "title": "Sojourn Ruin of a Two-Dimensional Fractional Brownian Motion Risk Process",
  "authors": [
    "Grigori Jasnovidov"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper derives the asymptotic behavior of $$\\mathbb{P} \\{ \\int\\limits_0^\\infty \\mathbb{I}\\Big(B_H(s)-c_1s>q_1u, B_H(s)-c_2s>q_2u\\Big)ds>T_u\\},\\quad u \\to \\infty,$$ where $B_H$ is a fractional Brownian motion, $c_1,c_2,q_1,q_2>0,\\ H \\in (0,1), \\ T_u \\ge 0$ is a measurable function and $\\mathbb{I}(\\cdot)$ is the indicator function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-23T16:01:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G70"
    ],
    "keywords": [
      "two-dimensional fractional brownian motion risk",
      "fractional brownian motion risk process",
      "sojourn ruin",
      "paper derives",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}