{
  "abstract": "We study stochastic flows with interaction through an infinite-dimensional semigroup approach. By means of a kernel lifting procedure, we represent the solution to measure-valued stochastic equation as a Hilbert-valued Markov process. We identify its generator, construct the associated Markov semigroup, and establish a dense range condition using measure polynomial functionals. The results provide a framework for the analysis of stability of stochastic equations with interaction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06924",
  "author_total": 1,
  "authors": [
    {
      "name": "Yifan Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4tsc9wchw4nhc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06924",
  "fulltext_url": null,
  "id": "4tsc9wchw4nhc",
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  "landing_url": "https://arxiv.org/abs/2610.06924",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  ],
  "openalex": "W7221036422",
  "pdf_url": "https://arxiv.org/pdf/2610.06924",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4tsc9wchw4nhc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.06924",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06924"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Complexity of flows with interactions and stochastic analysis",
  "title_text": "Complexity of flows with interactions and stochastic analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/4tsc9wchw4nhc",
  "venue": "arXiv",
  "versions": []
}