{"paper":{"title":"Mean-Field Backward Doubly Stochastic Differential Equations and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Qingfeng Zhu, Tianxiao Wang, Yufeng Shi","submitted_at":"2011-08-29T14:59:29Z","abstract_excerpt":"Mean-field backward doubly stochastic differential equations (MF-BDSDEs, for short) are introduced and studied. The existence and uniqueness of solutions for MF-BDSDEs is established. One probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs, for short) is given. A Pontryagin's type maximum principle is established for optimal control problem of MF-BDSDEs. Finally, one backward linear quadratic problem of mean-field type is discussed to illustrate the direct application of above maximum principle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5590","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"}