{
  "id": "2411.09949",
  "version": "v1",
  "published": "2024-11-15T05:02:50.000Z",
  "updated": "2024-11-15T05:02:50.000Z",
  "title": "$W_{\\bf d}$-convergence rate of EM schemes for invariant measures of supercritical stable SDEs",
  "authors": [
    "Peng Chen",
    "Lihu Xu",
    "Xiaolong Zhang",
    "Xicheng Zhang"
  ],
  "comment": "24",
  "categories": [
    "math.PR"
  ],
  "abstract": "By establishing the regularity estimates for nonlocal Stein/Poisson equations under $\\gamma$-order H\\\"older and dissipative conditions on the coefficients, we derive the $W_{\\bf d}$-convergence rate for the Euler-Maruyama schemes applied to the invariant measure of SDEs driven by multiplicative $\\alpha$-stable noises with $\\alpha \\in (\\frac{1}{2}, 2)$, where $W_{\\bf d}$ denotes the Wasserstein metric with ${\\bf d}(x,y)=|x-y|^\\gamma\\wedge 1$ and $\\gamma \\in ((1-\\alpha)_+, 1]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-15T05:02:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10"
    ],
    "keywords": [
      "invariant measure",
      "supercritical stable sdes",
      "convergence rate",
      "em schemes",
      "nonlocal stein/poisson equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}