{"paper":{"title":"Random time with differentiable conditional distribution function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Shiqi Song","submitted_at":"2013-12-19T19:17:58Z","abstract_excerpt":"Given a stochastic structure with a filtration $\\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\\mathbb{F}$ adapted non decreasing processes is considered. The main property of a random time in this class is that it can be isomorphically implanted into an auxiliary model which is absolutely continuous with respect to a Cox model. Three formulas are established: the conditional expectation formula, the optional splitting formula, and the enlargement of filtration formula. This study is particularly useful for models wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5709","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"}