{"paper":{"title":"Necessary and sufficient conditions for the $r$-excessive local martingales to be martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mihail Zervos, Mikhail Urusov","submitted_at":"2016-12-26T14:17:22Z","abstract_excerpt":"We consider the decreasing and the increasing $r$-excessive functions $\\varphi_r$ and $\\psi_r$ that are associated with a one-dimensional conservative regular continuous strong Markov process $X$ with values in an interval with endpoints $\\alpha < \\beta$. We prove that the $r$-excessive local martingale $\\bigl( e^{-r (t \\wedge T_\\alpha)} \\varphi_r (X_{t \\wedge T_\\alpha}) \\bigr)$ $\\bigl($resp., $\\bigl( e^{-r (t \\wedge T_\\beta)} \\psi_r (X_{t \\wedge T_\\beta}) \\bigr) \\bigr)$ is a strict local martingale if the boundary point $\\alpha$ (resp., $\\beta$) is inaccessible and entrance, and a martingale "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08387","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"}