{"paper":{"title":"Asymptotic analysis of exit time for dynamical systems with a single well potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.AP","authors_text":"D. Borisov, O. Sultanov","submitted_at":"2019-06-11T17:37:28Z","abstract_excerpt":"We study the exit time from a bounded multi-dimensional domain $\\Omega$\n  of the stochastic process $\\mathbf{Y}_\\varepsilon=\\mathbf{Y}_\\varepsilon(t,a)$, $t\\geqslant 0$, $a\\in \\mathcal{A}$, governed by the overdamped Langevin dynamics \\begin{equation*}\n  d\\mathbf{Y}_\\varepsilon =-\\nabla V(\\mathbf{Y}_\\varepsilon) dt +\\sqrt{2}\\varepsilon\\, d\\mathbf{W}, \\qquad \\mathbf{Y}_\\varepsilon(0,a)\\equiv x\\in\\Omega \\end{equation*} where $\\varepsilon$ is a small positive parameter, $\\mathcal{A}$ is a sample space, $\\mathbf{W}$ is a $n$-dimensional Wiener process. The exit time corresponds to the first hittin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04715","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"}