{
  "id": "1507.05202",
  "version": "v1",
  "published": "2015-07-18T16:22:16.000Z",
  "updated": "2015-07-18T16:22:16.000Z",
  "title": "Couplings of Brownian Motions of deterministic distance in the Euclidean space and on the sphere",
  "authors": [
    "Mihai N. Pascu",
    "Ionel Popescu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We obtain a characterization of all co-adapted couplings of Brownian motions in the Euclidean space and on the unit spheres in Euclidean spaces whose distance process is deterministic. More precisely, we show that there exists a co-adapted coupling of Brownian motions on these spaces for which the distance between the processes is a deterministic function if and only if the given function is continuous and satisfies almost everywhere a certain differential inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-18T16:22:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euclidean space",
      "brownian motions",
      "deterministic distance",
      "unit spheres",
      "distance process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150705202P"
    }
  }
}