{"paper":{"title":"Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Alain Durmus (LTCI), Eric Moulines (CMAP)","submitted_at":"2015-07-17T16:23:23Z","abstract_excerpt":"In this paper, we study a method to sample from a target  distribution $\\pi$ over $\\mathbb{R}^d$ having a positive density with  respect to the Lebesgue measure, known up to a  normalisation factor. This method is based on the Euler  discretization of the overdamped Langevin stochastic differential  equation associated with $\\pi$. For both constant and decreasing  step sizes in the Euler discretization, we obtain non-asymptotic  bounds for the convergence to the target distribution $\\pi$ in total  variation distance. A particular attention is paid to the dependency  on the dimension $d$, to de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05021","kind":"arxiv","version":3},"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"}