{"paper":{"title":"Extended Conditional G-Expectations and Related Stopping Times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mingshang Hu, Shige Peng","submitted_at":"2013-09-16T04:42:04Z","abstract_excerpt":"In this paper we extend the definition of time conditional G-expectations $\\mathbb{\\hat{E}}_{t}[\\cdot]$ to a larger domain on which the dynamical consistency still holds. In fact we can consistently define, by taking the limit, the time conditional expectations for each random variable $X$ which is the downward limit (resp. upward limit) of a monotone sequence $\\{X_{i}\\}$ in $L_{G}^{1}(\\Omega)$. To accomplish this procedure, some careful analysis is needed. Moreover, we give a suitable definition of stopping times and obtain the optional stopping theorem. We also provide some basic and interes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3829","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"}