{
  "id": "math/0606392",
  "version": "v1",
  "published": "2006-06-16T13:19:35.000Z",
  "updated": "2006-06-16T13:19:35.000Z",
  "title": "Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process",
  "authors": [
    "Manuel Lladser",
    "Jaime San Martin"
  ],
  "comment": "11 pages",
  "journal": "J. Appl. Probab. 37, no. 2 (2000), 511-521",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Let $X=(X_t)$ be a one-dimensional Ornstein-Uhlenbeck process with an initial density function $f$ supported on the positive real-line that is a regularly varying function with exponent $-(1+\\eta)$, with $\\eta\\in (0,1)$. We prove the existence of a probability measure $\\nu$ with a Lebesgue density, depending on $\\eta$, such that for every Borel set $A$ of the positive real-line: $\\lim_{t\\to\\infty} P_f(X_t\\in A | T_0^X>t)=\\nu(A)$, where $T_0^X$ is the hitting time of 0 of $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-16T13:19:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "65C30"
    ],
    "keywords": [
      "quasi-stationary distributions",
      "attraction",
      "initial density function",
      "one-dimensional ornstein-uhlenbeck process",
      "positive real-line"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6392L"
    }
  }
}