{"paper":{"title":"Remarks on non-linear noise excitability of some stochastic heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mathew Joseph, Mohammud Foondun","submitted_at":"2014-02-01T12:52:55Z","abstract_excerpt":"We consider nonlinear parabolic SPDEs of the form $\\partial_t u=\\Delta u + \\lambda \\sigma(u)\\dot w$ on the interval $(0, L)$, where $\\dot w$ denotes space-time white noise, $\\sigma$ is Lipschitz continuous. Under Dirichlet boundary conditions and a linear growth condition on $\\sigma$, we show that the expected $L^2$-energy is of order $\\exp[\\text{const}\\times\\lambda^4]$ as $\\lambda\\rightarrow \\infty$. This significantly improves a recent result of Khoshnevisan and Kim. Our method is very different from theirs and it allows us to arrive at the same conclusion for the same equation but with Neum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0084","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":""},"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"}