{
  "id": "1403.3714",
  "version": "v2",
  "published": "2014-03-14T22:05:24.000Z",
  "updated": "2015-04-17T14:19:25.000Z",
  "title": "Hitting times of points for symmetric Lévy processes with completely monotone jumps",
  "authors": [
    "Tomasz Juszczyszyn",
    "Mateusz Kwaśnicki"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Small-space and large-time estimates and asymptotic expansion of the distribution function and (the derivatives of) the density function of hitting times of points for symmetric L\\'evy processes are studied. The L\\'evy measure is assumed to have completely monotone density function, and a scaling-type condition inf z Psi\"(z) / Psi'(z) > 0 is imposed on the L\\'evy-Khintchine exponent Psi. Proofs are based on generalised eigenfunction expansion for processes killed upon hitting the origin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-14T22:05:24.000Z",
      "abstract": "Small-space and large-time estimates and asymptotic expansion of the distribution function and (the derivatives of) the density function of hitting times of points for symmetric L\\'evy processes are studied. The L\\'evy measure is assumed to have completely monotone density function, and a scaling-type condition inf z Psi''(z) / Psi'(z) > 0 is imposed on the L\\'evy-Khintchine exponent Psi. Proofs are based on generalised eigenfunction expansion for processes killed upon hitting the origin.",
      "comment": "20 pages",
      "journal": null,
      "doi": null,
      "authors": [
        "T. Juszczyszyn",
        "M. Kwaśnicki"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-04-17T14:19:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric lévy processes",
      "hitting times",
      "monotone jumps",
      "levy-khintchine exponent psi",
      "symmetric levy processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.3714J"
    }
  }
}