{"paper":{"title":"Functional It\\=o calculus in Hilbert spaces and application to path-dependent Kolmogorov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Mauro Rosestolato","submitted_at":"2016-06-20T20:47:35Z","abstract_excerpt":"Recently, functional It\\=o calculus has been introduced and developed in finite dimension for functionals of continuous semimartingales. With different techniques, we develop a functional It\\=o calculus for functionals of Hilbert spacevalued diffusions. In this context, we first prove a path-dependent It\\=o's formula, then we show applications to classical solutions of path-dependent Kolmogorov equations in Hilbert spaces and derive a Clark-Ocone type formula. Finally, we explicitly verify that all the theory developed can be applied to a class of diffusions driven by SDEs with a path-dependen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06326","kind":"arxiv","version":3},"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"}