{"paper":{"title":"Nonparametric estimation of the characteristic triplet of a discretely observed L\\'evy process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Shota Gugushvili","submitted_at":"2008-07-22T13:00:43Z","abstract_excerpt":"Given a discrete time sample $X_1,... X_n$ from a L\\'evy process $X=(X_t)_{t\\geq 0}$ of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet $(\\gamma,\\sigma^2,\\rho)$ corresponding to the process $X.$ Based on Fourier inversion and kernel smoothing, we propose estimators of $\\gamma,\\sigma^2$ and $\\rho$ and study their asymptotic behaviour. The obtained results include derivation of upper bounds on the mean square error of the estimators of $\\gamma$ and $\\sigma^2$ and an upper bound on the mean integrated square error of an estimator of $\\rho.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3469","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"}