{
  "id": "2204.10941",
  "version": "v1",
  "published": "2022-04-22T21:48:27.000Z",
  "updated": "2022-04-22T21:48:27.000Z",
  "title": "Reflected Brownian Motion with Drift in a Wedge",
  "authors": [
    "Peter Lakner",
    "Ziran Liu",
    "Josh Reed"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study reflecting Brownian motion with drift constrained to a wedge in the plane. Our first set of results provide necessary and sufficient conditions for existence and uniqueness of a solution to the corresponding submartingale problem with drift, and show that its solution possesses the Markov and Feller properties. Next, we study a version of the problem with absorption at the vertex of the wedge. In this case, we provide a condition for existence and uniqueness of a solution to the problem and some results on the probability of the vertex being reached.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-22T21:48:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reflected brownian motion",
      "study reflecting brownian motion",
      "feller properties",
      "first set",
      "solution possesses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}