{"paper":{"title":"Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian--fractional Brownian model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ehsan Azmoodeh, Lauri Viitasaari, Tommi Sottinen","submitted_at":"2014-11-17T14:48:52Z","abstract_excerpt":"We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter $H$ of the fractional part satisfies $H\\in(3/4,1)$, the central limit theorem holds. In the nonsemimartingale case, that is, where $H\\in(1/2,3/4]$, the convergence toward the normal distribution with a nonzero mean still holds if $H=3/4$, whereas for the other values, that is, $H\\in(1/2,3/4)$, the central convergence does not take place. We also provide Berry--Esseen estimates for the estima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4499","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"}