{"paper":{"title":"Regularization by noise and flows of solutions for a stochastic heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Leonid Mytnik, Oleg Butkovsky","submitted_at":"2016-10-08T16:34:45Z","abstract_excerpt":"Motivated by the regularization by noise phenomenon for SDEs we prove existence and uniqueness of the flow of solutions for the non-Lipschitz stochastic heat equation $$\\frac{\\partial u}{\\partial t}=\\frac12\\frac{\\partial^2 u}{\\partial z^2} + b(u(t,z)) + \\dot{W}(t,z), $$ where $\\dot W$ is a space-time white noise on $\\mathbb{R}_+\\times\\mathbb{R}$ and $b$ is a bounded measurable function on $\\mathbb{R}$. As a byproduct of our proof we also establish the so-called path--by--path uniqueness for any initial condition in a certain class on the same set of probability one. This extends recent results"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02553","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"}