{
  "id": "2501.10820",
  "version": "v1",
  "published": "2025-01-18T16:46:18.000Z",
  "updated": "2025-01-18T16:46:18.000Z",
  "title": "Functional limit theorems for a time-changed multidimensional Wiener process",
  "authors": [
    "Yuliia Mishura",
    "René L. Schilling"
  ],
  "comment": "14 pages. arXiv admin note: text overlap with arXiv:2005.04122",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process itself. At the level of generators, the time change means that we consider the Laplace operator -- which generates a multidimensional Wiener process -- and multiply it by a (possibly degenerate) state-space dependent intensity. We assume that the intensity admits limits at infinity in each octant of the state space, but the values of these limits may be different. Applying a functional limit theorem for the superposition of stochastic processes, we prove functional limit theorems for the normalized time-changed multidimensional Wiener process. Among the possible limits there is a multidimensional analogue of skew Brownian motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-18T16:46:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60J60",
      "60J55",
      "60F05",
      "60F17"
    ],
    "keywords": [
      "functional limit theorem",
      "normalized time-changed multidimensional wiener process",
      "skew brownian motion",
      "intensity admits limits",
      "state-space dependent intensity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}