{"paper":{"title":"Functional it{\\^o} versus banach space stochastic calculus and strict solutions of semilinear path-dependent equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrea Cosso (LPMA), Francesco Russo (ENSTA ParisTech UMA)","submitted_at":"2015-05-12T09:29:31Z","abstract_excerpt":"Functional It\\^o calculus was introduced in order to expand a functional $F(t, X\\_{\\cdot+t}, X\\_t)$ depending on time $t$, past and present values of the process $X$. Another possibility to expand $F(t, X\\_{\\cdot+t}, X\\_t)$ consists in considering the path $X\\_{\\cdot+t}=\\{X\\_{x+t},\\,x\\in[-T,0]\\}$ as an element of the Banach space of continuous functions on $C([-T,0])$ and to use Banach space stochastic calculus.\nThe aim of  this paper is threefold. \n1) To reformulate functional It\\^o calculus, separating time and past, making use of the regularization procedures which matches more naturally th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02926","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"}