{"paper":{"title":"On the continuity of the probabilistic representation of a semilinear Neumann-Dirichlet problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aurel R\\u{a}\\c{s}canu, Lucian Maticiuc","submitted_at":"2013-09-19T11:27:42Z","abstract_excerpt":"In this article we prove the continuity of the deterministic function $u:[0,T]\\times \\mathcal{\\bar{D}}\\rightarrow \\mathbb{R}$, defined by $u(t,x):=Y_{t}^{t,x}$, where the process $(Y_{s}^{t,x})_{s\\in[t,T]}$ is given by the generalized multivalued backward stochastic differential equation: \\begin{equation*} \\left\\{ \\begin{array}{l} -dY_{s}^{t,x}+\\partial \\varphi(Y_{s}^{t,x})ds+\\partial\\psi(Y_{s}^{t,x})dA_{s}^{t,x}\\ni f(s,X_{s}^{t,x},Y_{s}^{t,x})ds \\\\ \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;+g(s,X_{s}^{t,x},Y_{s}^{t,x})dA_{s}^{t,x}-Z_{s}^{t,x}dW_{s}~,\\;t\\leq s < T, \\\\ {Y_{T}=h(X_{T}^{t,x}).} \\end{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4935","kind":"arxiv","version":4},"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"}