{
  "id": "1411.6476",
  "version": "v1",
  "published": "2014-11-24T14:59:42.000Z",
  "updated": "2014-11-24T14:59:42.000Z",
  "title": "Weak error analysis for semilinear stochastic Volterra equations with additive noise",
  "authors": [
    "Adam Andersson",
    "Mihály Kovács",
    "Stig Larsson"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "We prove a weak error estimate for the approximation in space and time of a semilinear stochastic Volterra integro-differential equation driven by additive space-time Gaussian noise. We treat this equation in an abstract framework, in which parabolic stochastic partial differential equations are also included as a special case. The approximation in space is performed by a standard finite element method and in time by an implicit Euler method combined with a convolution quadrature. The weak rate of convergence is proved to be twice the strong rate, as expected. Our weak convergence result concerns not only the solution at a fixed time but also integrals of the entire path with respect to any finite Borel measure. The proof does not rely on a Kolmogorov equation. Instead it is based on a duality argument from Malliavin calculus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-24T14:59:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H07",
      "65C30",
      "65M60"
    ],
    "keywords": [
      "semilinear stochastic volterra equations",
      "weak error analysis",
      "stochastic partial differential equations",
      "stochastic volterra integro-differential equation",
      "volterra integro-differential equation driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.6476A"
    }
  }
}