{
  "id": "1604.04645",
  "version": "v1",
  "published": "2016-04-15T21:13:33.000Z",
  "updated": "2016-04-15T21:13:33.000Z",
  "title": "Location of the Path Supremum for Self-similar Processes with Stationary Increments",
  "authors": [
    "Yi Shen"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. To this end, a point process is constructed and its relation to the distribution of the location of the path supremum is studied. Using this framework, we show that the distribution has a spectral-type representation, in the sense that it is always a mixture of a special group of absolutely continuous distributions, plus point masses on the two boundaries. Bounds on the value and the derivatives of the density function are established. We further discuss self-similar L\\'{e}vy processes as an example. Most of the results in this paper can be generalized to a group of random locations, including the location of the largest jump, etc.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-15T21:13:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G18",
      "60G55",
      "60G10"
    ],
    "keywords": [
      "path supremum",
      "self-similar processes",
      "stationary increments",
      "distribution",
      "plus point masses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404645S"
    }
  }
}