{
  "id": "2408.03853",
  "version": "v1",
  "published": "2024-08-07T15:50:32.000Z",
  "updated": "2024-08-07T15:50:32.000Z",
  "title": "Recurrence of multidimensional affine recursions in the critical case",
  "authors": [
    "Richard Aoun",
    "Sara Brofferio",
    "Marc Peigné"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove, under different natural hypotheses, that the random multidimensional affine recursion $X_n=A_nX_{n-1}+B_n\\in\\mathbb{R}^d, n \\geq 1,$ is recurrent in the critical case. In particular we cover the cases where the matrices $A_n$ are similarities, invertible, rank 1 or with non negative coefficients. These results are a consequence of a criterion of recurrence for a large class of affine recursions on $\\mathbb R^d$, based on some moment assumptions of the so-called ``reverse norm control random variable\".",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-07T15:50:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60F17",
      "60K37"
    ],
    "keywords": [
      "critical case",
      "recurrence",
      "random multidimensional affine recursion",
      "reverse norm control random variable",
      "non negative coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}