{
  "id": "1105.1055",
  "version": "v1",
  "published": "2011-05-05T12:51:51.000Z",
  "updated": "2011-05-05T12:51:51.000Z",
  "title": "G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics",
  "authors": [
    "Shige Peng"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We provide a general approach to construct a stochastic process with a given consistent family of finite dimensional distributions under a nonlinear expectation space. We use this approach to construct a generalized Gaussian process under a sublinear expectation and a q-Brownian motion. The later one is under a complex-valued linear expectation, with which a new type of Feynman-Kac formula can be derived to represent the solution of a Schr\\\"odinger equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-05T12:51:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60J65",
      "46N50"
    ],
    "keywords": [
      "sublinear expectation",
      "q-brownian motion",
      "g-gaussian processes",
      "quantum mechanics",
      "finite dimensional distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.1055P"
    }
  }
}