{
  "id": "2202.12579",
  "version": "v1",
  "published": "2022-02-25T09:35:46.000Z",
  "updated": "2022-02-25T09:35:46.000Z",
  "title": "Convex hulls of stable random walks",
  "authors": [
    "Wojciech Cygan",
    "Nikola Sandrić",
    "Stjepan Šebek"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in $\\mathbb{R}^d$. We prove convergence of the convex hull in the space of all convex and compact subsets of $\\mathbb{R}^d$, equipped with the Hausdorff distance, towards the convex hull spanned by a path of the limit stable L\\'{e}vy process. As an application, we establish convergence of (expected) intrinsic volumes under some mild moment/structure assumptions posed on the random walk.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-25T09:35:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60D05",
      "60F05",
      "60G52"
    ],
    "keywords": [
      "convex hull",
      "stable random walks",
      "mild moment/structure assumptions",
      "steps belong",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}