{"paper":{"title":"Derivative for the intersection local time of fractional Brownian Motions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Litan Yan","submitted_at":"2014-03-17T14:08:25Z","abstract_excerpt":"Let $B^{H_1}$ and $\\tilde{B}^{H_2}$ be two independent fractional Brownian motions on ${\\mathbb R}$ with respective indices $H_i\\in (0,1)$ and $H_1\\leq H_2$. In this paper, we consider their intersection local time $\\ell_t(a)$. We show that $\\ell_t(a)$ is differentiable in the spatial variable if $\\frac1{H_1}+\\frac1{H_2}>3$, and we introduce the so-called {\\it hybrid quadratic covariation} $[f(B^{H_1}-\\tilde{B}^{H_2}),B^{H_1}]^{(HC)}$. When $H_1<\\frac12$, we construct a Banach space ${\\mathscr H}$ of measurable functions such that the quadratic covariation exists in $L^2(\\Omega)$ for all $f\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4102","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"}