{
  "id": "math/0601699",
  "version": "v2",
  "published": "2006-01-28T02:34:58.000Z",
  "updated": "2007-01-10T03:45:15.000Z",
  "title": "Multi-Dimensional G-Brownian Motion and Related Stochastic Calculus under G-Expectation",
  "authors": [
    "Shige Peng"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We develop a notion of nonlinear expectation --G-expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first study multi-dimensional G-normal distributions. With this nonlinear distribution we can introduce our G-expectation under which the canonical process is a multi dimensional G-Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Ito's type with respect to our G-Brownian motion and derive the related Ito's formula. We have also obtained the existence and uniqueness of stochastic differential equation under our G-expectation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-10T03:45:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H05",
      "60H30",
      "60J60",
      "60J65"
    ],
    "keywords": [
      "related stochastic calculus",
      "multi-dimensional g-brownian motion",
      "g-expectation",
      "first study multi-dimensional g-normal distributions",
      "multi dimensional g-brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1699P"
    }
  }
}