{"paper":{"title":"SPDEs with Polynomial Growth Coefficients and Malliavin Calculus Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Huaizhong Zhao, Qi Zhang","submitted_at":"2011-11-09T13:28:11Z","abstract_excerpt":"In this paper we study the existence and uniqueness of the $L_{\\rho}^{2p}(\\mathbb{R}^d;\\mathbb{R}^1)\\times L_{\\rho}^2(\\mathbb{R}^d;\\mathbb{R}^d)$ valued solution of backward doubly stochastic differential equations with polynomial growth coefficients using week convergence, equivalence of norm principle and Wiener-Sobolev compactness arguments. Then we establish a new probabilistic representation of the weak solutions of SPDEs with polynomial growth coefficients through the solutions of the corresponding backward doubly stochastic differential equations (BDSDEs). This probabilistic representat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2202","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"}