{"paper":{"title":"Deterministic and Stochastic Differential Equations in Hilbert Spaces Involving Multivalued Maximal Monotone Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Aurel Rascanu","submitted_at":"2014-02-04T14:41:28Z","abstract_excerpt":"This work deals with a Skorokhod problem driven by a maximal operator: \\begin{aligned} &du(t)+Au(t)(dt)\\ni f(t)dt+dM(t), \\; 0<t<T,\\\\ &u(0)=u_{0}, \\end{aligned} which is a multivalued deterministic differential equation with a singular inputs $dM(t)$, where $t\\rightarrow M(t)$ is a continuous function.\n  The existence and uniqueness result is used to study an It\\^{o}'s stochastic differential equation \\begin{aligned} &du(t)+Au(t)(dt)\\ni f(t,u(t))dt+B(t,u(t))dW(t),\\; 0<t<T,\\\\ &u(0)=u_{0}, \\end{aligned} in a real Hilbert space $H$, where $A$ is a multivalued ($\\alpha$-)maximal monotone operator o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0748","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"}