{
  "id": "1708.07683",
  "version": "v1",
  "published": "2017-08-25T10:42:37.000Z",
  "updated": "2017-08-25T10:42:37.000Z",
  "title": "A radial invariance principle for non-homogeneous random walks",
  "authors": [
    "Nicholas Georgiou",
    "Aleksandar Mijatović",
    "Andrew R. Wade"
  ],
  "comment": "10 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider non-homogeneous zero-drift random walks in $\\mathbb{R}^d$, $d \\geq 2$, with the asymptotic increment covariance matrix $\\sigma^2 (\\mathbf{u})$ satisfying $\\mathbf{u}^\\top \\sigma^2 (\\mathbf{u}) \\mathbf{u} = U$ and $\\mathrm{tr}\\ \\sigma^2 (\\mathbf{u}) = V$ in all in directions $\\mathbf{u}\\in\\mathbb{S}^{d-1}$ for some positive constants $U<V$. In this paper we establish weak convergence of the radial component of the walk to a Bessel process with dimension $V/U$. This can be viewed as an extension of an invariance principle of Lamperti.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-25T10:42:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J05",
      "60F17",
      "60J60"
    ],
    "keywords": [
      "radial invariance principle",
      "non-homogeneous random walks",
      "asymptotic increment covariance matrix",
      "non-homogeneous zero-drift random walks",
      "radial component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}