{
  "id": "2404.16485",
  "version": "v1",
  "published": "2024-04-25T10:18:01.000Z",
  "updated": "2024-04-25T10:18:01.000Z",
  "title": "Concentration estimates for SPDEs driven by fractional Brownian motion",
  "authors": [
    "Nils Berglund",
    "Alexandra Blessing"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The main goal of this work is to provide sample-path estimates for the solution of slowly time-dependent SPDEs perturbed by a cylindrical fractional Brownian motion. Our strategy is similar to the approach by Berglund and Nader for space-time white noise. However, the setting of fractional Brownian motion does not allow us to use any martingale methods. Using instead optimal estimates for the probability that the supremum of a Gaussian process exceeds a certain level, we derive concentration estimates for the solution of the SPDE, provided that the Hurst index $H$ of the fractional Brownian motion satisfies $H>\\frac14$. As a by-product, we also obtain concentration estimates for one-dimensional fractional SDEs valid for any $H\\in(0,1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-25T10:18:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G17",
      "60H15"
    ],
    "keywords": [
      "concentration estimates",
      "spdes driven",
      "fractional brownian motion satisfies",
      "one-dimensional fractional sdes valid",
      "cylindrical fractional brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}