{
  "id": "1510.03684",
  "version": "v1",
  "published": "2015-10-13T14:10:33.000Z",
  "updated": "2015-10-13T14:10:33.000Z",
  "title": "On the discretization in time of the stochastic Allen-Cahn equation",
  "authors": [
    "Mihály Kovács",
    "Stig Larsson",
    "Fredrik Lindgren"
  ],
  "comment": "34 pages",
  "categories": [
    "math.NA",
    "math.PR"
  ],
  "abstract": "We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension $d\\le 3$, and study the semidiscretisation in time of the equation by an Euler type split step method. We show that the method converges strongly with a rate $O(\\Delta t^{\\gamma}) $ for any $\\gamma<\\frac12$. By means of a perturbation argument, we also establish the strong convergence of the standard backward Euler scheme with the same rate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-13T14:10:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H35",
      "65C30"
    ],
    "keywords": [
      "stochastic allen-cahn equation",
      "euler type split step method",
      "discretization",
      "smooth additive gaussian noise",
      "standard backward euler scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151003684K"
    }
  }
}