{"paper":{"title":"On occupation times of the first and third quadrants for planar Brownian motion","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Larry Shepp, Philip Ernst","submitted_at":"2016-02-24T17:24:15Z","abstract_excerpt":"An open problem of interest, first infused into the applied probability community in the work of Bingham and Doney in 1988, (see \\cite{Bingham}) is stated as follows: find the distribution of the quadrant occupation time of planar Brownian motion. In this short communication, we study an alternate formulation of this longstanding open problem: let $X(t), Y(t), t \\geq 0$ be standard Brownian motions starting at $x,y$ respectively. Find the distribution of the total time $T=Leb\\{t \\in [0,1]: X(t) \\times Y(t) >0\\}$, when $x=y=0$, i.e., the occupation time of the union of the first and third quadr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07605","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"}