{
  "id": "1505.03391",
  "version": "v1",
  "published": "2015-05-13T14:00:21.000Z",
  "updated": "2015-05-13T14:00:21.000Z",
  "title": "An invariance principle for stochastic heat equations with periodic coefficients",
  "authors": [
    "Lu Xu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we investigate the asymptotic behaviors of solution $u(t, \\cdot)$ of a stochastic heat equation with a periodic nonlinear term. Such equation appears related to the dynamical sine-Gordon model. We consider the reversible case and extend the central limit theorem for diffusions in finite dimensions to infinite dimensional settings. Due to our results, as $t \\rightarrow \\infty$, $\\frac{1}{\\sqrt{t}}u(t, \\cdot)$ converges weakly to a centered Gaussian variable whose covariance operator is explicitly described. Different from the finite dimensional case, the fluctuation in $x$ vanishes in the limit distribution. Furthermore, we verify the tightness and present an invariance principle for $\\{\\epsilon u(\\epsilon^{-2}t, \\cdot)\\}_{t \\in [0, T]}$ as $\\epsilon \\downarrow 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-13T14:00:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60H15"
    ],
    "keywords": [
      "stochastic heat equation",
      "invariance principle",
      "periodic coefficients",
      "periodic nonlinear term",
      "central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150503391X"
    }
  }
}