{
  "abstract": "We develop a functional-analytic theory of convergence for non-symmetric generalized Dirichlet forms defined on a sequence of Hilbert spaces $H_n$ converging to a limit space $H$ in the sense of Kuwae-Shioya, with the principal applications concerning $L^2$-spaces over varying reference measures $μ_n \\to μ$. Extending Mosco's variational convergence for Dirichlet forms to the non-symmetric setting via a functional controlling the off diagonal values of the forms, we introduce a notion of generalized convergence of non-symmetric Dirichlet forms and show it to be equivalent to strong convergence of the associated resolvents, to weak convergence of the co-resolvents, and to strong graph convergence of the infinitesimal generators. A version of the Trotter-Kato theorem in the Kuwae-Shioya framework yields the corresponding equivalence for $C_0$-contraction semigroups. As applications, we give sufficient conditions for the generalized convergence of elliptic and sectorial $a_{i,j}$-forms with changing speed measures, both on $\\mathbb{R}^d$ and in infinite dimensions over a Gelfand triple, and deduce weak convergence of the laws of the associated right processes under tightness of the path measures.",
  "abstract_shown": true,
  "affiliations": [
    "( JMT) Aalto University , Department of Mathematics and Systems Analysis , PO Box 11100 ( Otakaari 1 , Espoo ), 00076 Aalto , Finland",
    "Department of Mathematics and Statistics"
  ],
  "article_type": null,
  "arxiv": "2611.00975",
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Jonas M. Tölle",
      "orcid": "0000-0002-6020-4131"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqskp37hzdv7b.bib",
  "cited_by": 9,
  "doi": "10.48550/arxiv.2611.00975",
  "fulltext_url": null,
  "id": "aqskp37hzdv7b",
  "issns": [
    "2331-8422"
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  "landing_url": "https://arxiv.org/abs/2611.00975",
  "language": "en",
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  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "math.AP"
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  "pdf_url": "https://arxiv.org/pdf/2611.00975",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": "Cornell University",
  "ris": "https://research.draconitic.com/paper/aqskp37hzdv7b.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00975",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00975"
    },
    {
      "first_seen": "2026-11-06T13:20:21Z",
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      "url": "https://arxiv.org/abs/2611.00975"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Convergence of non-symmetric forms with changing reference measures",
  "title_text": "Convergence of non-symmetric forms with changing reference measures",
  "type": "preprint",
  "updated_at": "2026-11-06T13:20:21Z",
  "url": "https://research.draconitic.com/paper/aqskp37hzdv7b",
  "venue": "arXiv",
  "versions": []
}