{"paper":{"title":"On distributions determined by their upward, space-time Wiener-Hopf factor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lo\\\"ic Chaumont, Ron Doney","submitted_at":"2017-01-31T22:04:07Z","abstract_excerpt":"According to the Wiener-Hopf factorization, the characteristic function $\\varphi$ of any probability distribution $\\mu$ on $\\mathbb{R}$ can be decomposed in a unique way as \\[1-s\\varphi(t)=[1-\\chi_-(s,it)][1-\\chi_+(s,it)]\\,,\\;\\;\\;|s|\\le1,\\,t\\in\\mathbb{R}\\,,\\] where $\\chi_-(e^{iu},it)$ and $\\chi_+(e^{iu},it)$ are the characteristic functions of possibly defective distributions in $\\mathbb{Z}_+\\times(-\\infty,0)$ and $\\mathbb{Z}_+\\times[0,\\infty)$, respectively.\n  We prove that $\\mu$ can be characterized by the sole data of the upward factor $\\chi_+(s,it)$, $s\\in[0,1)$, $t\\in\\mathbb{R}$ in many c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00067","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"}