{
  "id": "0910.5119",
  "version": "v2",
  "published": "2009-10-27T13:57:56.000Z",
  "updated": "2021-07-05T11:08:40.000Z",
  "title": "An inequality for a class of Markov processes",
  "authors": [
    "Mohammud Foondun"
  ],
  "comment": "Now irrelevant paper",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\alpha \\in (0,2)$ and consider the operator $\\sL$ given by \\[ \\sL f(x)=\\int[ f(x+h)-f(x)-1_{(|h|\\leq 1)}h\\cdot \\grad f(x)]\\frac{n(x,h)}{|h|^{d+\\alpha}} \\d h, \\] where the term $1_{(|h|\\leq 1)}h\\cdot \\grad f(x)$ is not present when $\\alpha \\in (0,1)$. Under some suitable assumptions on the kernel $n(x,h)$, we prove a Krylov-type inequality for processes associated with $\\sL$. As an application of the inequality, we prove the existence of a solution to the martingale problem for $\\sL$ without assuming any continuity of $n(x,h)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-27T13:57:56.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2021-07-05T11:08:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10"
    ],
    "keywords": [
      "markov processes",
      "krylov-type inequality",
      "martingale problem",
      "suitable assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.5119F"
    }
  }
}