{
  "id": "2309.16271",
  "version": "v1",
  "published": "2023-09-28T09:09:39.000Z",
  "updated": "2023-09-28T09:09:39.000Z",
  "title": "Excursion theory for the Wright-Fisher diffusion",
  "authors": [
    "Paul A. Jenkins",
    "Jere Koskela",
    "Jaromir Sant",
    "Dario Spano",
    "Ivana Valentic"
  ],
  "comment": "19 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this work, we develop excursion theory for the Wright-Fisher diffusion with recurrent mutation. Our construction is intermediate between the classical excursion theory where all excursions begin and end at a single point and the more general approach considering excursions of processes from general sets. Since the Wright-Fisher diffusion has two boundary points, it is natural to construct excursions which start from a specified boundary point, and end at one of two boundary points which determine the next starting point. In order to do this we study the killed Wright-Fisher diffusion, which is sent to a cemetery state whenever it hits either endpoint. We then construct a marked Poisson process of such killed paths which, when concatenated, produce a pathwise construction of the Wright-Fisher diffusion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-28T09:09:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J70",
      "60J60",
      "92D25",
      "60J55"
    ],
    "keywords": [
      "general approach considering excursions",
      "general sets",
      "construction",
      "excursions begin",
      "single point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}