{"paper":{"title":"Integral with respect to the $G$-Brownian local time","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Bo Gao, Litan Yan, Xichao Sun","submitted_at":"2012-12-27T11:43:13Z","abstract_excerpt":"Let ${\\mathscr L}$ be the local time of $G$-Brownian motion $B$. In this paper, we prove the existence of the quadratic covariation $<f(B),B>_{t}$ and the integral $\\int_{\\mathbb R}f(x){\\mathscr L}(dx,t)$. Moreover, a sublinear version of the Bouleau-Yor identity $$ \\int_{\\mathbb R}f(x){\\mathscr L}(dx,t)=-<f(B),B>_{t} $$ is showed to hold under some suitable conditions. These allow us to write the It\\^o's formula for $C^1$-functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6353","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"}