{
  "id": "1706.04132",
  "version": "v1",
  "published": "2017-06-13T15:38:17.000Z",
  "updated": "2017-06-13T15:38:17.000Z",
  "title": "On Martingale Problems and Feller Processes",
  "authors": [
    "Franziska Kühn"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $A$ be a pseudo-differential operator with negative definite symbol $q$. In this paper we establish a sufficient condition such that the well-posedness of the $(A,C_c^{\\infty}(\\mathbb{R}^d))$-martingale problem implies that the unique solution to the martingale problem is a Feller process. This provides a proof of a former claim by van Casteren. As an application we prove new existence and uniqueness results for L\\'evy-driven stochastic differential equations and stable-like processes with unbounded coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-13T15:38:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25"
    ],
    "keywords": [
      "feller process",
      "levy-driven stochastic differential equations",
      "martingale problem implies",
      "negative definite symbol",
      "unique solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}