{
  "id": "2412.09145",
  "version": "v1",
  "published": "2024-12-12T10:29:40.000Z",
  "updated": "2024-12-12T10:29:40.000Z",
  "title": "Asymptotic expansions for normal deviations of random walks conditioned to stay positive",
  "authors": [
    "Denis Denisov",
    "Alexander Tarasov",
    "Vitali Wachtel"
  ],
  "comment": "40 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a one-dimensional random walk $S_n$ having i.i.d. increments with zero mean and finite variance. We continue our study of asymptotic expansions for local probabilities $\\mathbf P(S_n=x,\\tau_0>n)$, which has been started in \\cite{DTW23}. Obtained there expansions make sense in the zone $x=o(\\frac{\\sqrt{n}}{\\log^{1/2} n})$ only. In the present paper we derive an alternative expansion, which deals with $x$ of order $\\sqrt{n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-12T10:29:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60G40",
      "60F17"
    ],
    "keywords": [
      "asymptotic expansions",
      "normal deviations",
      "stay positive",
      "one-dimensional random walk",
      "zero mean"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}