{
  "id": "1505.05061",
  "version": "v1",
  "published": "2015-05-19T16:04:07.000Z",
  "updated": "2015-05-19T16:04:07.000Z",
  "title": "High-order integrator for sampling the invariant distribution of a class of parabolic SPDEs with additive space-time noise",
  "authors": [
    "Charles-Edouard Bréhier",
    "Gilles Vilmart"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "We introduce an integrator to sample with high-order of accuracy the invariant distribution for a class of semilinear SPDEs driven by a additive space-time noise. Using a postprocessor, the scheme is a modification with negligible overhead of the standard linearized implicit Euler-Maruyama method. It has an improved order of convergence $r+1$, where $r$ is the order of convergence of the original method. An analysis is provided in finite dimension for nonlinear SDE problems, and in infinite dimension in a linear case. Numerical experiments, including the stochastic nonlinear heat equation with space-time noise confirm the theoretical findings and illustrate the efficiency of the approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-19T16:04:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H35",
      "37M25"
    ],
    "keywords": [
      "additive space-time noise",
      "invariant distribution",
      "high-order integrator",
      "parabolic spdes",
      "stochastic nonlinear heat equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150505061B"
    }
  }
}