{"paper":{"title":"Existence and uniqueness of solution to scalar BSDEs with $L\\exp\\left(\\mu\\sqrt{2\\log(1+L)}\\right)$-integrable terminal values: the critical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"ShengJun Fan, Ying Hu","submitted_at":"2019-04-04T19:34:10Z","abstract_excerpt":"In \\cite{HuTang2018ECP}, the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) when the terminal value is $L\\exp\\left(\\mu\\sqrt{2\\log(1+L)}\\right)$-integrable for a positive parameter $\\mu>\\mu_0$ with a critical value $\\mu_0$, and a counterexample is provided to show that the preceding integrability for $\\mu<\\mu_0$ is not sufficient to guarantee the existence of the solution. Afterwards, the uniqueness result (with $\\mu>\\mu_0$) is also given in \\cite{BuckdahnHuTang2018ECP} for the preceding BSDE under the uniformly Lipschitz condi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02761","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"}