{
  "id": "0712.4137",
  "version": "v2",
  "published": "2007-12-26T20:14:16.000Z",
  "updated": "2008-06-22T02:36:24.000Z",
  "title": "Uniqueness for the martingale problem associated with pure jump processes of variable order",
  "authors": [
    "Huili Tang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $L$ be the operator defined on $C^2$ functions by $$L f(x)=\\int[f(x+h)-f(x)-1_{(|h|\\leq 1)}\\nabla f(x)\\cdot h]\\frac{n(x,h)}{|h|^{d+\\alpha(x)}}dh.$$ This is an operator of variable order and the corresponding process is of pure jump type. We consider the martingale problem associated with $L$. Sufficient conditions for existence and uniqueness are given. Transition density estimates for $\\alpha$-stable processes are also obtained.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-22T02:36:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J75"
    ],
    "keywords": [
      "martingale problem",
      "pure jump processes",
      "variable order",
      "uniqueness",
      "pure jump type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.4137T"
    }
  }
}