{
  "id": "1309.0942",
  "version": "v2",
  "published": "2013-09-04T08:27:50.000Z",
  "updated": "2013-09-05T09:47:44.000Z",
  "title": "$Φ$-Entropy Inequality and Invariant Probability Measure for SDEs with Jump",
  "authors": [
    "Feng-Yu Wang"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "By using the $\\Phi$-entropy inequality derived in \\cite{Wu, Ch} for Poisson measures, the same type of inequality is established for a class of stochastic differential equations driven by purely jump L\\'evy processes. The semigroup $\\Phi$-entropy inequality for SDEs driven by Poisson point processes as well as a sharp result on the existence of invariant probability measures are also presented.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-05T09:47:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariant probability measure",
      "entropy inequality",
      "stochastic differential equations driven",
      "poisson point processes",
      "purely jump levy processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0942W"
    }
  }
}