{"paper":{"title":"Large deviations for the boundary local time of doubly reflected Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hongzhong Zhang, Martin Forde, Rohini Kumar","submitted_at":"2014-09-06T02:21:42Z","abstract_excerpt":"We compute a closed-form expression for the moment generating function $\\hat{f}(x;\\lambda,\\alpha)=\\frac{1}{\\lambda}\\mathbb{E}_x(e^{\\alpha L_{\\tau}})$, where $L_t$ is the local time at zero for standard Brownian motion with reflecting barriers at $0$ and $b$, and $\\tau \\sim \\mathrm{Exp}(\\lambda)$ is independent of $W$. By analyzing how and where $\\hat{f}(x;\\cdot,\\alpha)$ blows up in $\\lambda$, a large-time large deviation principle (LDP) for $L_t/t$ is established using a Tauberian result and the G\\\"{a}rtner-Ellis Theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1972","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"}