{"paper":{"title":"A Note on the Smoluchowski-Kramers Approximation for the Langevin Equation with Reflection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Konstantinos Spiliopoulos","submitted_at":"2010-04-18T17:43:39Z","abstract_excerpt":"According to the Smoluchowski-Kramers approximation, the solution of the equation ${\\mu}\\ddot{q}^{\\mu}_t=b(q^{\\mu}_t)-\\dot{q}^{\\mu}_t+{\\Sigma}(q^{\\mu}_t)\\dot{W}_t, q^{\\mu}_0=q, \\dot{q}^{\\mu}_0=p$ converges to the solution of the equation $\\dot{q}_t=b(q_t)+{\\Sigma}(q_t)\\dot{W}_t, q_0=q$ as {\\mu}->0. We consider here a similar result for the Langevin process with elastic reflection on the boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3043","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"}