{
  "id": "math/0702710",
  "version": "v1",
  "published": "2007-02-23T17:06:05.000Z",
  "updated": "2007-02-23T17:06:05.000Z",
  "title": "Hitting Probabilities for Systems of Non-Linear Stochastic Heat Equations with Additive Noise",
  "authors": [
    "Robert C. Dalang",
    "Davar Khoshnevisan",
    "Eulalia Nualart"
  ],
  "comment": "44 pages; submitted for publication",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a system of $d$ coupled non-linear stochastic heat equations in spatial dimension 1 driven by $d$-dimensional additive space-time white noise. We establish upper and lower bounds on hitting probabilities of the solution $\\{u(t, x)\\}_{t \\in \\mathbb{R}_+, x \\in [0, 1]}$, in terms of respectively Hausdorff measure and Newtonian capacity. We also obtain the Hausdorff dimensions of level sets and their projections. A result of independent interest is an anisotropic form of the Kolmogorov continuity theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-23T17:06:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60J45",
      "60G60"
    ],
    "keywords": [
      "hitting probabilities",
      "additive noise",
      "dimensional additive space-time white noise",
      "coupled non-linear stochastic heat equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2710D"
    }
  }
}