{
  "id": "1003.1876",
  "version": "v2",
  "published": "2010-03-09T14:08:14.000Z",
  "updated": "2011-02-09T15:30:06.000Z",
  "title": "Approximating the coefficients in semilinear stochastic partial differential equations",
  "authors": [
    "Markus Kunze",
    "Jan van Neerven"
  ],
  "comment": "Referee's comments have been incorporated",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We investigate, in the setting of UMD Banach spaces E, the continuous dependence on the data A, F, G and X_0 of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form dX(t) = [AX(t) + F(t,X(t))]dt + G(t,X(t))dW_H(t), X(0)=X_0, where W_H is a cylindrical Brownian motion on a Hilbert space H. We prove continuous dependence of the compensated solutions X(t)-e^{tA}X_0 in the norms L^p(\\Omega;C^\\lambda([0,T];E)) assuming that the approximating operators A_n are uniformly sectorial and converge to A in the strong resolvent sense, and that the approximating nonlinearities F_n and G_n are uniformly Lipschitz continuous in suitable norms and converge to F and G pointwise. Our results are applied to a class of semilinear parabolic SPDEs with finite-dimensional multiplicative noise.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-09T15:30:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "47D06"
    ],
    "keywords": [
      "semilinear stochastic partial differential equations",
      "approximating",
      "semilinear stochastic evolution equations",
      "coefficients",
      "semilinear parabolic spdes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1876K"
    }
  }
}