{
  "id": "0711.1302",
  "version": "v1",
  "published": "2007-11-08T15:54:13.000Z",
  "updated": "2007-11-08T15:54:13.000Z",
  "title": "Local probabilities for random walks conditioned to stay positive",
  "authors": [
    "Vladimir Vatutin",
    "Vitali Wachtel"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let S_0=0,{S_n, n>0} be a random walk generated by a sequence of i.i.d. random variables X_1,X_2,... and let \\tau^{-} be the first descending ladder epoch. Assuming that the distribution of X_1 belongs to the domain of attraction of an \\alpha-stable law we study the asymptotic behavior of the local probabilities P(\\tau ^{-}=n) and the conditional local probabilities P(S_n\\in [x,x+y)|\\tau^{-}>n) for fixed y and x=x(n)\\in (0,\\infty).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-08T15:54:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random walks",
      "stay positive",
      "conditional local probabilities",
      "first descending ladder epoch",
      "random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.1302V"
    }
  }
}