{"paper":{"title":"The Bouleau-Yor identity for a bi-fractional Brownian motion","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Bo Gao, Junfeng Liu, Litan Yan","submitted_at":"2012-12-27T11:16:03Z","abstract_excerpt":"Let $B$ be a bi-fractional Brownian motion with indices $H\\in (0,1),K\\in (0,1]$, $2HK=1$ and let ${\\mathscr L}(x,t)$ be its local time process. We construct a Banach space ${\\mathscr H}$ of measurable functions such that the quadratic covariation $[f(B),B]$ and the integral $\\int_{\\mathbb R}f(x){\\mathscr L}(dx,t)$ exist provided $f\\in {\\mathscr H}$. Moreover, the Bouleau-Yor identity $$ [f(B),B]_t=-2^{1-K}\\int_{\\mathbb R}f(x){\\mathscr L}(dx,t),\\qquad t\\geq 0, $$ holds for all $f\\in {\\mathscr H}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6347","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"}