{"paper":{"title":"Nonparametric inference for discretely sampled L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Shota Gugushvili","submitted_at":"2009-08-21T13:17:39Z","abstract_excerpt":"Given a sample from a discretely observed L\\'evy process $X=(X_t)_{t\\geq 0}$ of the finite jump activity, the problem of nonparametric estimation of the L\\'evy density $\\rho$ corresponding to the process $X$ is studied. An estimator of $\\rho$ is proposed that is based on a suitable inversion of the L\\'evy-Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of $\\rho$ over suitable classes of L\\'evy triplets. The corresponding lower bounds are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3121","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"}