{
  "id": "2102.04905",
  "version": "v1",
  "published": "2021-02-09T16:00:44.000Z",
  "updated": "2021-02-09T16:00:44.000Z",
  "title": "On telegraph processes, their first passage times and running extrema",
  "authors": [
    "Nikita Ratanov"
  ],
  "comment": "9 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note, we present some ideas for describing the distributions of the running maximum/minimum, first passage times and telegraphic meanders. Explicit formulae for joint distribution of the extrema, the number of velocity switches and the terminal position are derived using coupled integral equations technique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-09T16:00:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K99",
      "G.3"
    ],
    "keywords": [
      "first passage times",
      "telegraph processes",
      "running extrema",
      "coupled integral equations technique",
      "telegraphic meanders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}