{"paper":{"title":"Calibration of self-decomposable L\\'{e}vy models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Mathias Trabs","submitted_at":"2011-11-04T08:28:36Z","abstract_excerpt":"We study the nonparametric calibration of exponential L\\'{e}vy models with infinite jump activity. In particular our analysis applies to self-decomposable processes whose jump density can be characterized by the $k$-function, which is typically nonsmooth at zero. On the one hand the estimation of the drift, of the activity measure $\\alpha:=k(0+)+k(0-)$ and of analogous parameters for the derivatives of the $k$-function are considered and on the other hand we estimate nonparametrically the $k$-function. Minimax convergence rates are derived. Since the rates depend on $\\alpha$, we construct esti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1067","kind":"arxiv","version":4},"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"}