{
  "id": "1405.0075",
  "version": "v1",
  "published": "2014-05-01T01:29:14.000Z",
  "updated": "2014-05-01T01:29:14.000Z",
  "title": "A note on space-time Holder regularity of mild solutions to stochastic Cauchy problems in Lp-spaces",
  "authors": [
    "Rafael Serrano"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper revisits the H\\\"{o}lder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces $L^p(\\mathcal{O}),$ with $p\\geq 2$ and $\\mathcal{O}\\subset\\mathbb{R}^d$ a bounded domain. We find conditions on $p, \\beta$ and $\\gamma$ under which the mild solution has almost surely trajectories in $\\mathcal{C}^\\beta([0,T];\\mathcal{C}^\\gamma(\\bar{\\mathcal{O}})).$ These conditions do not depend on the Cameron-Martin Hilbert space associated with the driving cylindrical noise. The main tool of this study is a regularity result for stochastic convolutions in M-type 2 Banach spaces by Z. Brze\\'zniak (Stoch. Stoch. Rep. Vol. 61, Iss. 3-4, 1997).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-01T01:29:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "47D06",
      "35R15"
    ],
    "keywords": [
      "mild solution",
      "space-time holder regularity",
      "parabolic stochastic cauchy problems",
      "cameron-martin hilbert space",
      "paper revisits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0075S"
    }
  }
}