{
  "id": "math/0601035",
  "version": "v2",
  "published": "2006-01-03T08:20:24.000Z",
  "updated": "2006-12-31T15:27:04.000Z",
  "title": "G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type",
  "authors": [
    "Shige Peng"
  ],
  "comment": "Submited to Proceedings Abel Symposium 2005, Dedicated to Professor Kiyosi Ito for His 90th Birthday",
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a notion of nonlinear expectation --G--expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first discuss the notion of G-standard normal distribution. With this nonlinear distribution we can introduce our G-expectation under which the canonical process is a 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 give the existence and uniqueness of stochastic differential equation under our G-expectation. As compared with our previous framework of g-expectations, the theory of G-expectation is intrinsic in the sense that it is not based on a given (linear) probability space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-12-31T15:27:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H05",
      "60H30",
      "60J60",
      "60J65",
      "60A05",
      "60E05",
      "60G05",
      "60G51",
      "35K55",
      "35K15",
      "49L25"
    ],
    "keywords": [
      "related stochastic calculus",
      "g-brownian motion",
      "itos type",
      "g-expectation",
      "stochastic differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1035P"
    }
  }
}