{"paper":{"title":"Weak solutions of backward stochastic differential equations with continuous generator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nadira Bouchemella (LMRS), Paul Raynaud De Fitte (LMRS)","submitted_at":"2011-04-06T20:42:31Z","abstract_excerpt":"We prove the existence of a weak solution to a backward stochastic differential equation (BSDE) $$ Y_t=\\xi+\\int_t^T f(s,X_s,Y_s,Z_s)\\,ds-\\int_t^T Z_s\\,d\\wien_s$$ in a finite-dimensional space, where $f(t,x,y,z)$ is affine with respect to $z$, and satisfies a sublinear growth condition and a continuity condition This solution takes the form of a triplet $(Y,Z,L)$ of processes defined on an extended probability space and satisfying $$ Y_t=\\xi+\\int_t^T f(s,X_s,Y_s,Z_s)\\,ds-\\int_t^T Z_s\\,d\\wien_s-(L_T-L_t)$$ where $L$ is a continuous martingale which is orthogonal to any $\\wien$. The solution is c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1192","kind":"arxiv","version":4},"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"}