{
  "abstract": "We prove existence and uniqueness of a strong initial trace for every bounded kinetic solution of a stochastic scalar conservation law, although no initial value is prescribed and no nondegeneracy condition is imposed on the flux. The core of the proof is pathwise. After fixing a realization, the rescaled stochastic terms and kinetic measure vanish in the blow-up limit, so Panov's compactness argument applies; degenerate flux intervals are handled by recursive dimension reduction. The stochastic setting creates several additional difficulties. The martingale identities must remain valid on one common full-probability set throughout the reductions, which requires a parameterized stochastic-Fubini construction. Moreover, the pathwise trace is not automatically measurable because its exceptional sets may depend on the realization. Deterministic time averages and right-continuity of the filtration yield a jointly measurable initial trace, with local strong convergence along essential times, both almost surely and in mean.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20735",
  "author_total": 4,
  "authors": [
    {
      "name": "Marko Erceg"
    },
    {
      "name": "Kenneth Karlsen"
    },
    {
      "name": "Nikola Konatar"
    },
    {
      "name": "Darko Mitrovic"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/657mxjavaxbbe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20735",
  "fulltext_url": null,
  "id": "657mxjavaxbbe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20735",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7213599989",
  "pdf_url": "https://arxiv.org/pdf/2609.20735",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/657mxjavaxbbe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.20735",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20735"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Existence of strong initial traces for stochastic conservation laws",
  "title_text": "Existence of strong initial traces for stochastic conservation laws",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/657mxjavaxbbe",
  "venue": "arXiv",
  "versions": []
}