{
  "abstract": "In this article, we consider a Feller process whose resolvent has the strong Feller property. Using the Dynkin operator of this process, we define local realizations of the generator on an open subset $U$ of its state space. In particular, this allows us to describe the generator of the process killed upon leaving a regular, open subset $U$ as a realization of a maximal operator subject to Dirichlet boundary conditions. Besides the definition via the Dynkin operator, we also consider other possible definitions of such a local realization: a definition in terms of the unkilled semigroup, a definition based on approximation with elements of the generator and a probabilistic definition using martingales. Under mild additional assumptions, we prove that all these definitions are equivalent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38761",
  "author_total": 2,
  "authors": [
    {
      "name": "Markus Kunze"
    },
    {
      "name": "Jonathan Mui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0yg2yybv3zch6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38761",
  "fulltext_url": null,
  "id": "0yg2yybv3zch6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38761",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38761",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0yg2yybv3zch6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38761",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38761"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Localization of generators of Markov processes via the Dynkin operator",
  "title_text": "Localization of generators of Markov processes via the Dynkin operator",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0yg2yybv3zch6",
  "venue": "arXiv",
  "versions": []
}