{
  "id": "1806.00745",
  "version": "v1",
  "published": "2018-06-03T07:34:54.000Z",
  "updated": "2018-06-03T07:34:54.000Z",
  "title": "Cramér's estimate for stable processes with power drift",
  "authors": [
    "Christophe Profeta",
    "Thomas Simon"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate the upper tail probabilities of the all-time maximum of a stable L\\'evy process with a power negative drift. The asymptotic behaviour is shown to be exponential in the spectrally negative case and polynomial otherwise, with explicit exponents and constants. Analogous results are obtained, at a less precise level, for the fractionally integrated stable L\\'evy process. We also study the lower tail probabilities of the integrated stable L\\'evy process in the presence of a power positive drift.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-03T07:34:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "power drift",
      "cramérs estimate",
      "stable processes",
      "upper tail probabilities",
      "lower tail probabilities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}