{
  "id": "1509.05677",
  "version": "v1",
  "published": "2015-09-18T15:59:03.000Z",
  "updated": "2015-09-18T15:59:03.000Z",
  "title": "Martin kernels for Markov processes with jumps",
  "authors": [
    "Tomasz Juszczyszyn",
    "Mateusz Kwaśnicki"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove existence of boundary limits of ratios of positive harmonic functions for a wide class of Markov processes with jumps and irregular domains, in the context of general metric measure spaces. As a corollary, we prove uniqueness of the Martin kernel at each boundary point, that is, we identify the Martin boundary with the topological boundary. We also prove a Martin representation theorem for harmonic functions. Examples covered by our results include: strictly stable L\\'evy processes in R^d with positive continuous density of the L\\'evy measure; stable-like processes in R^d and in domains; and stable-like subordinate diffusions in metric measure spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-18T15:59:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "martin kernel",
      "markov processes",
      "harmonic functions",
      "general metric measure spaces",
      "martin representation theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150905677J"
    }
  }
}