{
  "id": "0806.1898",
  "version": "v1",
  "published": "2008-06-11T15:49:45.000Z",
  "updated": "2008-06-11T15:49:45.000Z",
  "title": "The Stochastic Heat Equation Driven by a Gaussian Noise: germ Markov Property",
  "authors": [
    "Raluca Balan",
    "Doyoon Kim"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $u=\\{u(t,x);t \\in [0,T], x \\in {\\mathbb{R}}^{d}\\}$ be the process solution of the stochastic heat equation $u_{t}=\\Delta u+ \\dot F, u(0,\\cdot)=0$ driven by a Gaussian noise $\\dot F$, which is white in time and has spatial covariance induced by the kernel $f$. In this paper we prove that the process $u$ is locally germ Markov, if $f$ is the Bessel kernel of order $\\alpha=2k,k \\in \\bN_{+}$, or $f$ is the Riesz kernel of order $\\alpha=4k,k \\in \\bN_{+}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-11T15:49:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G60"
    ],
    "keywords": [
      "stochastic heat equation driven",
      "germ markov property",
      "gaussian noise",
      "bessel kernel",
      "locally germ markov"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.1898B"
    }
  }
}