{
  "id": "1506.05680",
  "version": "v1",
  "published": "2015-06-18T13:54:55.000Z",
  "updated": "2015-06-18T13:54:55.000Z",
  "title": "Efficient discretisation of stochastic differential equations",
  "authors": [
    "Masaaki Fukasawa",
    "Jan Obloj"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The aim of this study is to find a generic method for generating a path of the solution of a given stochastic differential equation which is more efficient than the standard Euler-Maruyama scheme with Gaussian increments. First we characterize the asymptotic distribution of pathwise error in the Euler-Maruyama scheme with a general partition of time interval and then, show that the error is reduced by a factor (d+2)/d when using a partition associated with the hitting times of sphere for the driving d-dimensional Brownian motion. This reduction ratio is the best possible in a symmetric class of partitions. Next we show that a reduction which is close to the best possible is achieved by using the hitting time of a moving sphere which is easier to implement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-18T13:54:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H35",
      "60F05"
    ],
    "keywords": [
      "stochastic differential equation",
      "efficient discretisation",
      "standard euler-maruyama scheme",
      "driving d-dimensional brownian motion",
      "hitting time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150605680F"
    }
  }
}