{
  "id": "0911.4681",
  "version": "v2",
  "published": "2009-11-24T17:26:54.000Z",
  "updated": "2010-03-10T19:19:02.000Z",
  "title": "Weak order for the discretization of the stochastic heat equation driven by impulsive noise",
  "authors": [
    "Felix Lindner",
    "René L. Schilling"
  ],
  "comment": "29 pages; Section 1 extended, new results in Appendix B",
  "categories": [
    "math.PR",
    "math.NA"
  ],
  "abstract": "Considering a linear parabolic stochastic partial differential equation driven by impulsive space time noise, dX_t+AX_t dt= Q^{1/2}dZ_t, X_0=x_0\\in H, t\\in [0,T], we approximate the distribution of X_T. (Z_t)_{t\\in[0,T]} is an impulsive cylindrical process and Q describes the spatial covariance structure of the noise; Tr(A^{-\\alpha})<\\infty for some \\alpha>0 and A^\\beta Q is bounded for some \\beta\\in(\\alpha-1,\\alpha]. A discretization (X_h^n)_{n\\in\\{0,1,...,N\\}} is defined via the finite element method in space (parameter h>0) and a \\theta-method in time (parameter \\Delta t=T/N). For \\phi\\in C^2_b(H;R) we show an integral representation for the error |E\\phi(X^N_h)-E\\phi(X_T)| and prove that |E\\phi(X^N_h)-E\\phi(X_T)|=O(h^{2\\gamma}+(\\Delta t)^{\\gamma}) where \\gamma<1-\\alpha+\\beta.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-10T19:19:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "65M60",
      "60H35",
      "60G51",
      "60G52",
      "65C30"
    ],
    "keywords": [
      "stochastic heat equation driven",
      "weak order",
      "impulsive noise",
      "linear parabolic stochastic partial differential",
      "stochastic partial differential equation driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.4681L"
    }
  }
}