{"paper":{"title":"On the density of the supremum of a stable process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexey Kuznetsov","submitted_at":"2011-12-19T00:47:26Z","abstract_excerpt":"We study the density of the supremum of a strictly stable L\\'evy process. As was proved recently in F. Hubalek and A. Kuznetsov \"A convergent series representation for the density of the supremum of a stable process\" (Elect. Comm. in Probab., 16, 84-95, 2011), for almost all irrational values of the stability parameter $\\alpha$ this density can be represented by an absolutely convergent series. We show that this result is not valid for all irrational values of $\\alpha$: we construct a dense uncountable set of irrational numbers $\\alpha$ for which the series does not converge absolutely. Our se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4208","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"}