{
  "id": "2101.03992",
  "version": "v1",
  "published": "2021-01-11T16:02:03.000Z",
  "updated": "2021-01-11T16:02:03.000Z",
  "title": "Lévy area without approximation",
  "authors": [
    "Isao Sauzedde"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We give asymptotic estimations on the area of the sets of points with large Brownian winding, and study the average winding between a planar Brownian motion and a Poisson point process of large intensity on the plane. This allows us to give a new definition of the L\\'evy area which does not rely on approximations of the Brownian path. It also does not depend on the metric structure on the plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-11T16:02:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "26B20",
      "60E07"
    ],
    "keywords": [
      "lévy area",
      "approximation",
      "poisson point process",
      "planar brownian motion",
      "asymptotic estimations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}