{"paper":{"title":"The Tamed Unadjusted Langevin Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Alain Durmus, \\'Eric Moulines, Nicolas Brosse, Sotirios Sabanis","submitted_at":"2017-10-16T08:32:28Z","abstract_excerpt":"In this article, we consider the problem of sampling from a probability measure $\\pi$ having a density on $\\mathbb{R}^d$ known up to a normalizing constant, $x\\mapsto \\mathrm{e}^{-U(x)} / \\int_{\\mathbb{R}^d} \\mathrm{e}^{-U(y)} \\mathrm{d} y$. The Euler discretization of the Langevin stochastic differential equation (SDE) is known to be unstable in a precise sense, when the potential $U$ is superlinear, i.e. $\\liminf_{\\Vert x \\Vert\\to+\\infty} \\Vert \\nabla U(x) \\Vert / \\Vert x \\Vert = +\\infty$. Based on previous works on the taming of superlinear drift coefficients for SDEs, we introduce the Tame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05559","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"}