{
  "id": "2004.12422",
  "version": "v1",
  "published": "2020-04-26T15:58:40.000Z",
  "updated": "2020-04-26T15:58:40.000Z",
  "title": "On a maximum of nearest-neighbor random walk with asymptotically zero drift on lattice of positive half line",
  "authors": [
    "Hongyan Sun",
    "Hua-Ming Wang"
  ],
  "comment": "10 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a nearest-neighbor random walk with certain asymptotically zero drift on the positive half line. Let $M$ be the maximum of an excursion starting from $1$ and ending at $0.$ We study the distribution of $M$ and characterize its asymptotics, which is quite different from those of simple random walks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-26T15:58:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60J10"
    ],
    "keywords": [
      "nearest-neighbor random walk",
      "positive half line",
      "asymptotically zero drift",
      "simple random walks",
      "distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}