{"paper":{"title":"Generalized covariation for Banach space valued processes, It\\^o formula and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cristina Di Girolami (LMM), Francesco Russo (ENSTA ParisTech, INRIA Rocquencourt)","submitted_at":"2010-12-11T19:44:08Z","abstract_excerpt":"This paper discusses a new notion of quadratic variation and covariation for Banach space valued processes (not necessarily semimartingales) and related It\\^o formula. If $\\X$ and $\\Y$ take respectively values in Banach spaces $B_{1}$ and $B_{2}$ and $\\chi$ is a suitable subspace of the dual of the projective tensor product of $B_{1}$ and $B_{2}$ (denoted by $(B_{1}\\hat{\\otimes}_{\\pi}B_{2})^{\\ast}$), we define the so-called $\\chi$-covariation of $\\X$ and $\\Y$. If $\\X=\\Y$, the $\\chi$-covariation is called $\\chi$-quadratic variation. The notion of $\\chi$-quadratic variation is a natural generali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2484","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"}