{
  "id": "2212.09919",
  "version": "v1",
  "published": "2022-12-19T23:58:02.000Z",
  "updated": "2022-12-19T23:58:02.000Z",
  "title": "Generating Functions for Asymmetric Random Walk Processes With Double Absorbing Barriers",
  "authors": [
    "Cetin Hakimoglu-Brown"
  ],
  "comment": "21 pages, 0 figures",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Generating functions for asymmetric step-size paths restricted by two absorbing barriers are derived. The method begins by applying the Lagrange inversion formula to arbitrary powers of roots of the characteristic equation, that being a trinomial, which produces generating function as function (z) of the conditional probability of absorption of a particle, on a path restricted by two absorbing barriers. The exact enumeration of an asymmetric walk with two absorbing barriers is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-19T23:58:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "G.2.1",
      "G.2.m",
      "G.3",
      "G.2"
    ],
    "keywords": [
      "asymmetric random walk processes",
      "generating function",
      "double absorbing barriers",
      "lagrange inversion formula",
      "method begins"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}