{"paper":{"title":"It\\^o Formula for Processes Taking Values in Intersection of Finitely Many Banach Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"David \\v{S}i\\v{s}ka, Istv\\'an Gy\\\"ongy","submitted_at":"2016-09-05T20:42:14Z","abstract_excerpt":"Motivated by applications to SPDEs we extend the It\\^o formula for the square of the norm of a semimartingale $y(t)$ from Gy\\\"ongy and Krylov (Stochastics 6(3):153-173, 1982) to the case \\begin{equation*} \\sum_{i=1}^m \\int_{(0,t]} v_i^{\\ast}(s)\\,dA(s) + h(t)=:y(t)\\in V \\quad \\text{$dA\\times \\mathbb{P}$-a.e.}, \\end{equation*} where $A$ is an increasing right-continuous adapted process, $v_i^{\\ast}$ is a progressively measurable process with values in $V_i^{\\ast}$, the dual of a Banach space $V_i$, $h$ is a cadlag martingale with values in a Hilbert space $H$, identified with its dual $H^{\\ast}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01320","kind":"arxiv","version":2},"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"}