{
  "id": "2005.06034",
  "version": "v1",
  "published": "2020-05-12T20:12:50.000Z",
  "updated": "2020-05-12T20:12:50.000Z",
  "title": "An adaptive Euler-Maruyama scheme for McKean SDEs with super-linear growth and application to the mean-field FitzHugh-Nagumo model",
  "authors": [
    "Christoph Reisinger",
    "Wolfgang Stockinger"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "math.PR"
  ],
  "abstract": "In this paper, we introduce a fully implementable, adaptive Euler-Maruyama scheme for McKean SDEs with non-globally Lipschitz continuous drifts. We prove moment stability of the discretised processes and a strong convergence rate of 1/2. We present several numerical examples centred around a mean-field model for FitzHugh-Nagumo neurons, which illustrate that the standard uniform scheme fails and that the adaptive scheme shows in most cases superior performance compared to tamed approximation schemes. In addition, we propose a tamed and an adaptive Milstein scheme for a certain class of McKean SDEs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-12T20:12:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adaptive euler-maruyama scheme",
      "mckean sdes",
      "mean-field fitzhugh-nagumo model",
      "super-linear growth",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}