{"paper":{"title":"Generalized covariation and extended Fukushima decompositions for Banach valued processes. Application to windows of Dirichlet processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cristina Di Girolami (Luiss Guido Carli), Francesco Russo (UMA)","submitted_at":"2011-05-23T07:33:17Z","abstract_excerpt":"This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of M\\'etivier and Pellaumail which is quite restrictive. We make use of the notion of $\\chi$-covariation which is a generalized notion of covariation for processes with values in two Banach spaces $B_{1}$ and $B_{2}$. $\\chi$ refers to a suitable subspace of the dual of the projective tensor product of $B_{1}$ and $B_{2}$. We investigate some $C^{1}$ type transformations for various classes of stochastic processes admitting a $\\chi$-quadratic va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4419","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"}