{
  "id": "math/0607022",
  "version": "v1",
  "published": "2006-07-03T18:49:32.000Z",
  "updated": "2006-07-03T18:49:32.000Z",
  "title": "Median, Concentration and Fluctuation for Lévy Processes",
  "authors": [
    "C. Houdré",
    "P. Marchal"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We estimate a median of $f(X_t)$ where $f$ is a Lipschitz function, $X$ is a L\\'evy process and $t$ an arbitrary time. This leads to concentration inequalities for $f(X_t)$. In turn, corresponding fluctuation estimates are obtained under assumptions typically satisfied if the process has a regular behavior in small time and a, possibly different, regular behavior in large time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-03T18:49:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E07",
      "60F10",
      "60G51",
      "60G52"
    ],
    "keywords": [
      "lévy processes",
      "regular behavior",
      "lipschitz function",
      "large time",
      "small time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7022H"
    }
  }
}