{"paper":{"title":"Non-uniqueness for non-negative solutions of parabolic stochastic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"C. Mueller, E.A. Perkins, K. Burdzy","submitted_at":"2010-08-12T15:04:10Z","abstract_excerpt":"Pathwise non-uniqueness is established for non-negative solutions of the parabolic stochastic pde $$\\frac{\\partial X}{\\partial t}=\\frac{\\Delta}{2}X+X^p\\dot W+\\psi,\\ X_0\\equiv 0$$ where $\\dot W$ is a white noise, $\\psi\\ge 0$ is smooth, compactly supported and non-trivial, and $0<p<1/2$. We further show that any solution spends positive time at the 0 function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2126","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}