{
  "abstract": "We study a multidimensional nonlinear filtering model whose coefficients depend on a given observation-adapted predictable process and whose observation drift may grow linearly in both the state and the random input. Due to the unboundedness of the observation drift, a global reference measure is not available. To overcome this hurdle, a localized entropy argument is adapted to prove the stopped likelihood to be a uniformly integrable martingale at each control-energy stopping level. The stopped Zakai equation, and hence, the stopped filtering equation is derived. The global filtering equation is then established by de-localization. The uniqueness of the solution to the stopped Zakai equation is obtained by a duality backward stochastic partial differential equation. This uniqueness then propagates to that of the global filtering equation through the stopped ones. Finally, a stability result is established in $W_1$-distance of measures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28985",
  "author_total": 3,
  "authors": [
    {
      "name": "Jie Xiong"
    },
    {
      "name": "Wen Xu"
    },
    {
      "name": "Ying Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09nz2tbpm5axp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28985",
  "fulltext_url": null,
  "id": "09nz2tbpm5axp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28985",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.28985",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09nz2tbpm5axp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28985",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28985"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Uniqueness and stability of nonlinear filtering equations with unbounded random coefficients",
  "title_text": "Uniqueness and stability of nonlinear filtering equations with unbounded random coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/09nz2tbpm5axp",
  "venue": "arXiv",
  "versions": []
}