{"paper":{"title":"Stochastic Control of Memory Mean-Field Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bernt {\\O}ksendal, Nacira Agram","submitted_at":"2017-01-07T08:36:52Z","abstract_excerpt":"By a memory mean-field process we mean the solution $X(\\cdot)$ of a stochastic mean-field equation involving not just the current state $X(t)$ and its law $\\mathcal{L}(X(t))$ at time $t$, but also the state values $X(s)$ and its law $\\mathcal{L}(X(s))$ at some previous times $s<t$. Our purpose is to study stochastic control problems of memory mean-field processes.\n  - We consider the space $\\mathcal{M}$ of measures on $\\mathbb{R}$ with the norm $|| \\cdot||_{\\mathcal{M}}$ introduced by Agram and {\\O}ksendal in \\cite{AO1}, and prove the existence and uniqueness of solutions of memory mean-field "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01801","kind":"arxiv","version":7},"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"}