{"paper":{"title":"A Donsker Theorem for L\\'evy Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Markus Rei\\ss, Richard Nickl","submitted_at":"2012-01-03T08:43:31Z","abstract_excerpt":"Given $n$ equidistant realisations of a L\\'evy process $(L_t,\\,t\\ge 0)$, a natural estimator $\\hat N_n$ for the distribution function $N$ of the L\\'evy measure is constructed. Under a polynomial decay restriction on the characteristic function $\\phi$, a Donsker-type theorem is proved, that is, a functional central limit theorem for the process $\\sqrt n (\\hat N_n -N)$ in the space of bounded functions away from zero. The limit distribution is a generalised Brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the Fourier-integral operator ${\\cal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0590","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"}