{"ID":23655416,"CreatedAt":"2026-09-18T07:57:10.708451858Z","UpdatedAt":"2026-09-18T07:57:10.708451858Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20735","arxiv_id":"2609.20735","title":"Existence of strong initial traces for stochastic conservation laws","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.","short_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 te...","url_abs":"https://arxiv.org/abs/2609.20735","url_pdf":"https://arxiv.org/pdf/2609.20735v1","authors":"[\"Marko Erceg\",\"Nikola Konatar\",\"Kenneth Karlsen\",\"Darko Mitrovic\"]","published":"2026-09-17T17:25:17Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.PR\"]","methods":"[]","has_code":false}