{"paper":{"title":"Bridges of L\\'{e}vy processes conditioned to stay positive","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ger\\'onimo Uribe Bravo","submitted_at":"2011-01-21T17:03:02Z","abstract_excerpt":"We consider Kallenberg's hypothesis on the characteristic function of a L\\'{e}vy process and show that it allows the construction of weakly continuous bridges of the L\\'{e}vy process conditioned to stay positive. We therefore provide a notion of normalized excursions L\\'{e}vy processes above their cumulative minimum. Our main contribution is the construction of a continuous version of the transition density of the L\\'{e}vy process conditioned to stay positive by using the weakly continuous bridges of the L\\'{e}vy process itself. For this, we rely on a method due to Hunt which had only been sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4184","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"}