{"paper":{"title":"A Note on a threshold for temporal regularity of stochastic PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antonio Agresti, Mark Veraar","submitted_at":"2025-09-09T14:44:15Z","abstract_excerpt":"We consider solutions to linear parabolic SPDEs of the form \\[ \\mathrm{d} u(t) + A u(t)\\, \\mathrm{d} t = g(t)\\, \\mathrm{d} \\beta, \\qquad u(0)=0, \\] where $A$ is a positive, invertible, and self-adjoint operator on a Hilbert space $X$, $\\beta$ is a one-dimensional Brownian motion, and $g(t)\\equiv x\\in X$. We show that, for all $\\alpha\\in [0,\\frac{1}{2}),$ \\[ u\\in L^2(\\Omega;W^{\\alpha,2}(0,T;\\mathsf{D}(A^{1/2}))) \\quad \\text{ if and only if }\\quad x\\in \\mathsf{D}(A^{\\alpha}). \\] In particular, there is a lack of persistence of temporal regularity from the diffusion coefficient $g$ to the solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07803","kind":"arxiv","version":3},"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/2509.07803/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"}