{
  "id": "2308.09432",
  "version": "v1",
  "published": "2023-08-18T10:04:59.000Z",
  "updated": "2023-08-18T10:04:59.000Z",
  "title": "Markov additive friendships",
  "authors": [
    "Leif Döring",
    "Lukas Trottner",
    "Alexander R. Watson"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The Wiener--Hopf factorisation of a L\\'evy or Markov additive process describes the way that it attains new maxima and minima in terms of a pair of so-called ladder height processes. Vigon's theory of friendship for L\\'evy processes addresses the inverse problem: when does a process exist which has certain prescribed ladder height processes? We give a complete answer to this problem for Markov additive processes, provide simpler sufficient conditions for constructing processes using friendship, and address in part the question of the uniqueness of the Wiener--Hopf factorisation for Markov additive processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-18T10:04:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60J25",
      "47A68"
    ],
    "keywords": [
      "markov additive friendships",
      "markov additive process",
      "wiener-hopf factorisation",
      "levy processes addresses",
      "prescribed ladder height processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}