{"paper":{"title":"Sparre-Andersen identity and the last passage time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jevgenijs Ivanovs","submitted_at":"2015-01-19T16:35:14Z","abstract_excerpt":"It is shown that the celebrated result of Sparre Andersen for random walks and L\\'evy processes has intriguing consequences when the last time of the process in $(-\\infty,0]$, say $\\sigma$, is added to the picture. In the case of no positive jumps this leads to six random times, all of which have the same distribution - the uniform distribution on $[0,\\sigma]$. Surprisingly, this result does not appear in the literature, even though it is based on some classical observations concerning exchangeable increments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04542","kind":"arxiv","version":2},"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"}