{"paper":{"title":"The distribution of the supremum for spectrally asymmetric L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Martijn Pistorius, Zbigniew Michna, Zbigniew Palmowski","submitted_at":"2014-10-09T18:10:14Z","abstract_excerpt":"In this article we derive formulas for the probability $P(\\sup_{t\\leq T} X(t)>u)$ $T>0$ and $P(\\sup_{t<\\infty} X(t)>u)$ where $X$ is a spectrally positive L\\'evy process with infinite variation. The formulas are generalizations of the well-known Tak\\'acs formulas for stochastic processes with non-negative and interchangeable increments. Moreover, we find the joint distribution of $\\inf_{t\\leq T} Y(t)$ and $Y(T)$ where $Y$ is a spectrally negative L\\'evy process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2554","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"}