{"paper":{"title":"Berry-Ess\\'een bounds and almost sure CLT for the quadratic variation of the bifractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Khalifa Es-Sebaiy, Soufiane Aazizi","submitted_at":"2012-03-13T12:42:23Z","abstract_excerpt":"Let $B$ be a bifractional Brownian motion with parameters $H\\in (0, 1)$ and $K\\in(0,1]$. For any $n\\geq1$, set $Z_n =\\sum_{i=0}^{n-1}\\big[n^{2HK}(B_{(i+1)/n}-B_{i/n})^2-\\E((B_{i+1}-B_{i})^2)\\big]$. We use the Malliavin calculus and the so-called Stein's method on Wiener chaos introduced by Nourdin and Peccati \\cite{NP09} to derive, in the case when $0<HK\\leq3/4$, Berry-Ess\\'een-type bounds for the Kolmogorov distance between the law of the correct renormalization $V_n$ of $Z_n$ and the standard normal law. Finally, we study almost sure central limit theorems for the sequence $V_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2786","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"}