Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9947-03-03450-0
Title: Uncorrelatedness and orthogonality for vector-valued processes
Authors: Loeb, P.A.
Osswald, H.
Sun, Y. 
Zhang, Z. 
Keywords: Keisler's pubini theorem
Loeb product space
Multilinear functional
Orthogonality
Uncorrelatedness
Vector-valued processes
Issue Date: Aug-2004
Citation: Loeb, P.A., Osswald, H., Sun, Y., Zhang, Z. (2004-08). Uncorrelatedness and orthogonality for vector-valued processes. Transactions of the American Mathematical Society 356 (8) : 3209-3225. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9947-03-03450-0
Abstract: For a square integrable vector-valued process f on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for f are presented. The process f is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for f involving the biorthogonal representation for the conditional expectation of f with respect to the usual product σ-algebra is presented.
Source Title: Transactions of the American Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/104420
ISSN: 00029947
DOI: 10.1090/S0002-9947-03-03450-0
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