{"paper":{"title":"Local times in a Brownian excursion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Krishna B. Athreya, Raoul Normand, Sheng-Jhih Wu, Vivekananda Roy","submitted_at":"2014-10-17T06:06:09Z","abstract_excerpt":"Let $\\{B(t), t \\geq 0\\}$ be a standard Brownian motion in $\\mathbb{R}$. Let $T$ be the first return time to 0 after hitting 1, and $\\{L(T,x), x \\in \\mathbb{R}\\}$ be the local time process at time $T$ and level $x$. The distribution of $L(T,x)$ for each $x \\in \\mathbb{R}$ is determined. This is applied to the estimation of a $L^1$ integral on $\\mathbb{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4643","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"}