{
  "id": "2004.10580",
  "version": "v1",
  "published": "2020-04-22T14:00:23.000Z",
  "updated": "2020-04-22T14:00:23.000Z",
  "title": "Multiscale schemes for stochastic dynamical systems driven by $α$-stable processes",
  "authors": [
    "Yanjie Zhang",
    "Xiao Wang",
    "Zibo Wang",
    "Jinqiao Duan"
  ],
  "categories": [
    "math.PR",
    "math.DS"
  ],
  "abstract": "This work is about strong and weak convergence of projective integration schemes for multiscale stochastic dynamical systems driven by $\\alpha$-stable processes. Firstly, we analyze a class of \"projective integration\" methods, which are used to estimate the effect that the fast components have on slow ones. Secondly, we obtain the $p$th moment error bounds between the results of the projective integration method and the slow components of the original system with $p \\in (1, \\min(\\alpha_1, \\alpha_2))$. Finally, a numerical experiment is constructed to illustrate this scheme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-22T14:00:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable processes",
      "multiscale schemes",
      "projective integration",
      "multiscale stochastic dynamical systems driven",
      "th moment error bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}