{
  "id": "1507.08466",
  "version": "v1",
  "published": "2015-07-30T11:55:09.000Z",
  "updated": "2015-07-30T11:55:09.000Z",
  "title": "Image sets of fractional Brownian sheets",
  "authors": [
    "Paul Balança"
  ],
  "comment": "14 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $B^H = \\{ B^H(t), t\\in\\mathbb{R}^N \\}$ be an $(N,d)$-fractional Brownian sheet with Hurst index $H=(H_1,\\dotsc,H_N)\\in (0,1)^N$. The main objective of the present paper is to study the Hausdorff dimension of the image sets $B^H(F+t)$, $F\\subset\\mathbb{R}^N$ and $t\\in\\mathbb{R}^N$, in the dimension case $d<\\tfrac{1}{H_1}+\\cdots+\\tfrac{1}{H_N}$. Following the seminal work of Kaufman (1989), we establish uniform dimensional properties on $B^H$, answering questions raised by Khoshnevisan et al (2006) and Wu and Xiao (2009). For the purpose of this work, we introduce a refinement of the sectorial local-nondeterminism property which can be of independent interest to the study of other fine properties of fractional Brownian sheets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-30T11:55:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional brownian sheet",
      "image sets",
      "sectorial local-nondeterminism property",
      "establish uniform dimensional properties",
      "independent interest"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}