{
  "id": "1103.4529",
  "version": "v1",
  "published": "2011-03-23T14:23:37.000Z",
  "updated": "2011-03-23T14:23:37.000Z",
  "title": "Ordered random walks with heavy tails",
  "authors": [
    "Denis Denisov",
    "Vitali Wachtel"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This note continues paper of Denisov and Wachtel (2010), where we have constructed a $k$-dimensional random walk conditioned to stay in the Weyl chamber of type $A$. The construction was done under the assumption that the original random walk has $k-1$ moments. In this note we continue the study of killed random walks in the Weyl chamber, and assume that the tail of increments is regularly varying of index $\\alpha<k-1$. It appears that the asymptotic behaviour of random walks is different in this case. We determine the asymptotic behaviour of the exit time, and, using thisinformation, construct a conditioned process which lives on a partial compactification of the Weyl chamber.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-23T14:23:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60G40",
      "60F17"
    ],
    "keywords": [
      "ordered random walks",
      "heavy tails",
      "weyl chamber",
      "asymptotic behaviour",
      "note continues paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.4529D"
    }
  }
}