{
  "id": "1910.12821",
  "version": "v1",
  "published": "2019-10-28T17:28:00.000Z",
  "updated": "2019-10-28T17:28:00.000Z",
  "title": "Spectral theory for one-dimensional (non-symmetric) stable processes killed upon hitting the origin",
  "authors": [
    "Jacek Mucha"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We obtain an integral formula for the distribution of the first hitting time of the origin for one-dimensional $\\alpha$-stable processes $X_t$, where $\\alpha\\in(1,2)$. We also find a spectral-type integral formula for the transition operators $P_0^t$ of $X_t$ killed upon hitting the origin. Both expressions involve exponentially growing oscillating functions, which play a role of generalised eigenfunctions for $P_0^t$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-28T17:28:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable processes",
      "spectral theory",
      "one-dimensional",
      "non-symmetric",
      "spectral-type integral formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}