{
  "id": "2102.04131",
  "version": "v1",
  "published": "2021-02-08T11:10:40.000Z",
  "updated": "2021-02-08T11:10:40.000Z",
  "title": "Higher Strong Order Methods for Itô SDEs on Matrix Lie Groups",
  "authors": [
    "Michelle Muniz",
    "Matthias Ehrhardt",
    "Michael Günther",
    "Renate Winkler"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper we present a general procedure for designing higher strong order methods for It\\^o stochastic differential equations on matrix Lie groups and illustrate this strategy with two novel schemes that have a strong convergence order of 1.5. Based on the Runge-Kutta--Munthe-Kaas (RKMK) method for ordinary differential equations on Lie groups, we present a stochastic version of this scheme and derive a condition such that the stochastic RKMK has the same strong convergence order as the underlying stochastic Runge-Kutta method. Further, we show how our higher order schemes can be applied in a mechanical engineering as well as in a financial mathematics setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-08T11:10:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "70G65",
      "91G80"
    ],
    "keywords": [
      "matrix lie groups",
      "strong convergence order",
      "designing higher strong order methods",
      "stochastic differential equations",
      "higher order schemes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}