{
  "id": "1906.09347",
  "version": "v1",
  "published": "2019-06-21T22:17:13.000Z",
  "updated": "2019-06-21T22:17:13.000Z",
  "title": "Logarithmic asymptotics for probability of component-wise ruin in two-dimensional Brownian model",
  "authors": [
    "Krzysztof Debicki",
    "Lanpeng Ji",
    "Tomasz Rolski"
  ],
  "comment": "17",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let ${\\bf X}({\\bf t})=(X_1(t),X_2(s)), {\\bf t}=(t,s)$ be a correlated two-dimensional Brownian motion and let $\\mu_1,\\mu_2>0$ be two constants. In this contribution, we derive the logarithmic asymptotics \\[ \\log P\\Bigl( \\sup_{t\\ge 0} \\Bigl( X_1(t) - \\mu_1 t\\Bigr)> u, \\ \\sup_{s\\ge 0} \\Bigl( X_2(s) - \\mu_2 s\\Bigr)> u \\Bigr),\\qquad u\\to\\infty. \\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-21T22:17:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional brownian model",
      "logarithmic asymptotics",
      "component-wise ruin",
      "probability",
      "correlated two-dimensional brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}