{
  "id": "1704.03501",
  "version": "v1",
  "published": "2017-04-11T19:08:04.000Z",
  "updated": "2017-04-11T19:08:04.000Z",
  "title": "Rules of calculus in the path integral representation of white noise Langevin equations",
  "authors": [
    "Leticia F. Cugliandolo",
    "Vivien Lecomte"
  ],
  "comment": "35 pages, 2 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The definition and manipulation of Langevin equations with multiplicative white noise require special care (one has to specify the time discretisation and a stochastic chain rule has to be used to perform changes of variables). While discretisation-scheme transformations and non-linear changes of variable can be safely performed on the Langevin equation, these same transformations lead to inconsistencies in its path-integral representation. We identify their origin and we show how to extend the well-known It\\=o prescription ($dB^2=dt$) in a way that defines a modified stochastic calculus to be used inside the path-integral representation of the process, in its Onsager-Machlup form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-11T19:08:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "white noise langevin equations",
      "path integral representation",
      "path-integral representation",
      "stochastic chain rule",
      "special care"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}