{"paper":{"title":"Probability that the maximum of the reflected Brownian motion over a finite interval $[0,t]$ is achieved by its last zero before $t$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Agn\\`es Lagnoux, Pierre Vallois, Sabine Mercier","submitted_at":"2015-05-13T08:34:31Z","abstract_excerpt":"We calculate the probability $p_c$ that the maximum of a reflected Brownian motion $U$ is achieved on a complete excursion, i.e. $p_c:=P\\big(\\overline{U}(t)=U^*(t)\\big)$ where $\\overline{U}(t)$ (respectively $U^*(t)$) is the maximum of the process $U$ over the time interval $[0,t]$ (resp. $\\big[0,g(t)\\big]$ where $g(t)$ is the last zero of $U$ before $t$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03274","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"}