{
  "id": "1006.0524",
  "version": "v4",
  "published": "2010-06-02T23:42:03.000Z",
  "updated": "2011-10-22T01:30:18.000Z",
  "title": "Spectral analysis of subordinate Brownian motions in half-line",
  "authors": [
    "Mateusz Kwasnicki"
  ],
  "comment": "58 pages, 1 figure. Major revision",
  "journal": "Studia Math. 206(3) (2011) 211-271",
  "doi": "10.4064/sm206-3-2",
  "categories": [
    "math.PR",
    "math.SP"
  ],
  "abstract": "We study one-dimensional Levy processes with Levy-Khintchine exponent psi(xi^2), where psi is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators, whose Levy measure has completely monotone density; or, equivalently, symmetric Levy processes whose Levy measure has completely monotone density on the positive half-line. Examples include symmetric stable processes and relativistic processes. The main result is a formula for the generalized eigenfunctions of transition operators of the process killed after exiting the half-line. A generalized eigenfunction expansion of the transition operators is derived. As an application, a formula for the distribution of the first passage time (or the supremum functional) is obtained.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-10-22T01:30:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47G30",
      "60G51",
      "60G52",
      "60J35"
    ],
    "keywords": [
      "subordinate brownian motions",
      "spectral analysis",
      "study one-dimensional levy processes",
      "transition operators",
      "levy measure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.0524K"
    }
  }
}