{
  "id": "1204.5050",
  "version": "v5",
  "published": "2012-04-23T12:59:44.000Z",
  "updated": "2018-01-07T22:30:10.000Z",
  "title": "A Multiplicative Ergodic Theorem for Discontinuous Random Dynamical Systems and Applications",
  "authors": [
    "Huijie Qiao",
    "Jinqiao Duan"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Motivated by studying stochastic systems with non-Gaussian L\\'evy noise, spectral properties for a type of linear cocycles are considered. These linear cocycles have countable jump discontinuities in time. A multiplicative ergodic theorem is proved for such linear cocycles. Then, the result is illustrated for two linear stochastic systems with general L\\'evy motions.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-02-17T08:56:55.000Z",
      "title": "Multiplicative Ergodic Theorem for Discontinuous Random Dynamical Systems and Applications",
      "abstract": "Motivated by studying stochastic systems with non-Gaussian L\\'evy noise, spectral properties for linear discontinuous cocycles are considered. These linear cocycles have countable jump discontinuities in time. A multiplicative ergodic theorem is proved for such linear cocycles. Then, the result is illustrated for a linear stochastic system with general L\\'evy motions. Finally, Lyapunov exponents are considered for linear stochastic differential equations with $\\alpha$-stable L\\'evy motions.",
      "comment": "23 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2018-01-07T22:30:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60G52",
      "47A35"
    ],
    "keywords": [
      "discontinuous random dynamical systems",
      "multiplicative ergodic theorem",
      "applications",
      "linear stochastic differential equations",
      "linear cocycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.5050Q"
    }
  }
}