{"paper":{"title":"Initial measures for the stochastic heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Conus, Davar Khoshnevisan, Mathew Joseph, Shang-Yuan Shiu","submitted_at":"2011-10-18T18:34:37Z","abstract_excerpt":"We consider a family of nonlinear stochastic heat equations of the form $\\partial_t u=\\mathcal{L}u + \\sigma(u)\\dot{W}$, where $\\dot{W}$ denotes space-time white noise, $\\mathcal{L}$ the generator of a symmetric L\\'evy process on $\\R$, and $\\sigma$ is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure $u_0$. Tight a priori bounds on the moments of the solution are also obtained.\n  In the particular case that $\\mathcal{L}f=cf\"$ for some $c>0$, we prove that if $u_0$ is a finite measure of compact support, then the sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4079","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"}