{"paper":{"title":"Integral representations of martingales for progressive enlargements of filtrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Aksamit, Marek Rutkowski, Monique Jeanblanc","submitted_at":"2015-12-13T02:58:27Z","abstract_excerpt":"We work in the setting of the progressive enlargement $\\mathbb G$ of a reference filtration $\\mathbb F$ through the observation of a random time $\\tau$. We study an integral representation property for some classes of $\\mathbb G$-martingales stopped at $\\tau$. In the first part, we focus on the case where $\\mathbb F$ is a Poisson filtration and we establish a predictable representation property with respect to three $\\mathbb G$-martingales. In the second part, we relax the assumption that $\\mathbb F$ is a Poisson filtration and we assume that $\\tau$ is an $\\mathbb F$-pseudo-stopping time. We e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03992","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"}