{
  "id": "2003.14381",
  "version": "v1",
  "published": "2020-03-31T17:25:07.000Z",
  "updated": "2020-03-31T17:25:07.000Z",
  "title": "Sample-path large deviations for unbounded additive functionals of the reflected random walk",
  "authors": [
    "Mihail Bazhba",
    "Jose Blanchet",
    "Chang-Han Rhee",
    "Bert Zwart"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove a sample path large deviation principle (LDP) with sub-linear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space equipped with the $M_1'$ topology. Our technique hinges on a suitable decomposition of the Markov chain in terms of regeneration cycles. Each regeneration cycle denotes the area accumulated during the busy period of the reflected random walk. We prove a large deviation principle for the area under the busy period of the MRW, and we show that it exhibits a heavy-tailed behavior.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-31T17:25:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G17"
    ],
    "keywords": [
      "reflected random walk",
      "sample-path large deviations",
      "unbounded additive functionals",
      "sample path large deviation principle",
      "regeneration cycle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}