{"paper":{"title":"Another look into the Wong-Zakai Theorem for Stochastic Heat Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Li-Cheng Tsai, Yu Gu","submitted_at":"2018-01-28T01:38:01Z","abstract_excerpt":"Consider the heat equation driven by a smooth, Gaussian random potential: \\begin{align*}\n  \\partial_t u_{\\varepsilon}=\\tfrac12\\Delta u_{\\varepsilon}+u_{\\varepsilon}(\\xi_{\\varepsilon}-c_{\\varepsilon}), \\ \\ t>0, x\\in\\mathbb{R}, \\end{align*} where $\\xi_{\\varepsilon}$ converges to a spacetime white noise, and $c_{\\varepsilon} $ is a diverging constant chosen properly. For any $ n\\geq 1 $, we prove that $ u_{\\varepsilon} $ converges in $ L^n $ to the solution of the stochastic heat equation. Our proof is probabilistic, hence provides another perspective of the general result of Hairer and Pardoux \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09164","kind":"arxiv","version":2},"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"}