{
  "id": "1207.5067",
  "version": "v2",
  "published": "2012-07-20T21:59:53.000Z",
  "updated": "2013-12-17T06:33:53.000Z",
  "title": "Simplified formulas for the mean and variance of linear stochastic differential equations",
  "authors": [
    "Juan Carlos Jimenez"
  ],
  "comment": "The new version has an improved introduction and a new numerical simulation study. In subsection 3.2, the difference between the new and previous results is pointed out as well as the relevance of the new result in some important applications",
  "categories": [
    "math.OC",
    "math.NA",
    "math.PR"
  ],
  "abstract": "Explicit formulas for the mean and variance of linear stochastic differential equations are derived in terms of an exponential matrix. This result improved a previous one by means of which the mean and variance are expressed in terms of a linear combination of higher dimensional exponential matrices. The important role of the new formulas for the system identification as well as numerical algorithms for their practical implementation are pointed out.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-17T06:33:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "93E11",
      "93E12"
    ],
    "keywords": [
      "linear stochastic differential equations",
      "simplified formulas",
      "higher dimensional exponential matrices",
      "explicit formulas",
      "linear combination"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.5067J"
    }
  }
}