{"paper":{"title":"Computing gaussian \\& exponential measures of semi-algebraic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean-Bernard Lasserre (LAAS-MAC)","submitted_at":"2015-08-25T12:38:18Z","abstract_excerpt":"We provide a numerical scheme to approximate as closely as desired the Gaussian or exponential measure $\\mu(\\om)$ of (not necessarily compact) basic semi-algebraic sets$\\om\\subset\\R^n$. We obtain two  monotone (non increasing and non decreasing) sequences of upper and lower bounds $(\\overline{\\omega}\\_d)$, $(\\underline{\\omega}\\_d)$, $d\\in\\N$, each converging to $\\mu(\\om)$ as $d\\to\\infty$. For each $d$, computing $\\overline{\\omega}\\_d$ or $\\underline{\\omega}\\_d$reduces to solving a semidefinite program whose size increases with $d$. Some preliminary (small dimension) computational experiments a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06132","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"}