{"paper":{"title":"Asymptotic properties of the derivative of self-intersection local time of fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arturo Jaramillo, David Nualart","submitted_at":"2015-12-22T19:50:28Z","abstract_excerpt":"Let $\\{B_{t}\\}_{t\\geq0}$ be a fractional Brownian motion with Hurst parameter $\\frac{2}{3}<H<1$. We prove that the approximation of the derivative of self-intersection local time, defined as \\begin{align*} \\alpha_{\\varepsilon} &= \\int_{0}^{T}\\int_{0}^{t}p'_{\\varepsilon}(B_{t}-B_{s})\\text{d}s\\text{d}t, \\end{align*} where $p_\\varepsilon(x)$ is the heat kernel, satisfies a central limit theorem when renormalized by $\\varepsilon^{\\frac{3}{2}-\\frac{1}{H}}$. We prove as well that for $q\\geq2$, the $q$-th chaotic component of $\\alpha_{\\varepsilon}$ converges in $L^{2}$ when $\\frac{2}{3}<H<\\frac{3}{4}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07219","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"}