{"paper":{"title":"The quadratic covariation for a weighted fractional Brownian motion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Litan Yan, Qinghua Zhang, Xichao Sun","submitted_at":"2016-03-05T12:38:12Z","abstract_excerpt":"Let $B^{a,b}$ be a weighted fractional Brownian motion with indices $a,b$ satisfying $a>-1,-1<b<0,|b|<1+a$. In this paper, motivated by the asymptotic property $$ E[(B^{a,b}_{s+\\varepsilon}-B^{a,b}_s)^2] =O(\\varepsilon^{1+b})\\not\\sim \\varepsilon^{1+a+b}=E[(B^{a,b}_{\\varepsilon})^2]\\qquad (\\varepsilon\\to 0) $$ for all $s>0$, we consider the generalized quadratic covariation $\\bigl[f(B^{a,b}),B^{a,b}\\bigr]^{(a,b)}$ defined by $$ \\bigl[f(B^{a,b}),B^{a,b}\\bigr]^{(a,b)}_t=\\lim_{\\varepsilon\\downarrow 0}\\frac{1+a+b}{\\varepsilon^{1+b}}\\int_\\varepsilon^{t+\\varepsilon} \\left\\{f(B^{a,b}_{s+\\varepsilon}) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01720","kind":"arxiv","version":1},"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"}