{
  "id": "2008.08219",
  "version": "v1",
  "published": "2020-08-19T01:49:17.000Z",
  "updated": "2020-08-19T01:49:17.000Z",
  "title": "Monte Carlo construction of cubature on Wiener space",
  "authors": [
    "Satoshi Hayakawa",
    "Ken'ichiro Tanaka"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "In this paper, we investigate application of mathematical optimization to construction of a cubature formula on Wiener space, which is a weak approximation method of stochastic differential equations introduced by Lyons and Victoir (Cubature on Wiener Space, Proc. R. Soc. Lond. A 460, 169--198). After giving a brief review of the cubature theory on Wiener space, we show that a cubature formula of general dimension and degree can be obtained through a Monte Carlo sampling and linear programming. This paper also includes an extension of stochastic Tchakaloff's theorem, which technically yields the proof of our main result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-19T01:49:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wiener space",
      "monte carlo construction",
      "cubature formula",
      "stochastic tchakaloffs theorem",
      "stochastic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}