{
  "id": "1510.01247",
  "version": "v1",
  "published": "2015-10-05T17:19:47.000Z",
  "updated": "2015-10-05T17:19:47.000Z",
  "title": "Stochastic differential equations revisited",
  "authors": [
    "Dietrich Ryter"
  ],
  "comment": "Replaces arXiv 1308.4515 and 1403.1060",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "The solution of the SDE follows the \"trend\" of the Fokker-Planck equation, which consists of the drift (given by the SDE) and of a term with derivatives of the diffusion. That extra term must be included in the stochastic integration. This yields the Ito sense of the SDE, while the FPE belongs to the anti-Ito sense and preserves important features of the case with a constant diffusion. An existing inconsistency is thereby removed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-05T17:19:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10"
    ],
    "keywords": [
      "stochastic differential equations",
      "preserves important features",
      "extra term",
      "fokker-planck equation",
      "constant diffusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}