{"paper":{"title":"Multivalued Stochastic Delay Differential Equations and Related Stochastic Control Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bakarime Diomande, Lucian Maticiuc","submitted_at":"2013-05-30T04:57:17Z","abstract_excerpt":"We study the existence and uniqueness of a solution for the multivalued stochastic differential equation with delay (the multivalued term is of subdifferential type): \\[ \\left\\{\\begin{array} [c]{r} dX(t)+\\partial\\varphi\\left(X(t)\\right) dt\\ni b\\left(t,X(t),Y(t),Z(t)\\right) dt+\\sigma\\left(t,X(t),Y(t),Z(t)\\right)dW(t), \\medskip\\\\ t\\in(s,T],\\medskip\\\\ \\multicolumn{1}{l}{X(t)=\\xi\\left(t-s\\right) ,\\;t\\in\\left[ s-\\delta,s\\right] .} \\end{array} \\right. \\]\n  Specify that in this case the coefficients at time $t$ depends also on previous values of $X\\left(t\\right) $ through $Y(t)$ and $Z(t)$. Also $X$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7003","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"}