{"paper":{"title":"On Skorokhod Problems for Reflected and Singular Stochastic Heat Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Martin Grothaus, Nicolas Renner","submitted_at":"2026-06-10T11:25:58Z","abstract_excerpt":"We prove a Skorokhod decomposition for the Markov processes $X^a$ and $X$ associated to the gradient Dirichlet forms with respect to the measures $\\rho^a\\mu^{\\beta}$ and $\\rho\\mu^{\\beta}$, respectively. Here, $\\mu^{\\beta}$ is the law of the standard Brownian bridge $\\beta$, while $\\rho^a$ and $\\rho$ denote densities which are given by $\\rho^a(z) := \\mathbf{1}_{[0,\\infty)}(\\bar{z}_a)$ and $\\rho(z) := \\int_0^1 \\mathbf{1}_{[0,\\infty)}(\\bar{z}_x) \\, dx$, respectively, for all $z\\in L^2(0,1)$ which have a (unique) continuous representative $\\bar{z}$ which vanishes at zero and one. To this end, we d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11951","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11951/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}