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|Title:||Uncorrelatedness and orthogonality for vector-valued processes|
|Keywords:||Keisler's pubini theorem|
Loeb product space
|Source:||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|
|Appears in Collections:||Staff Publications|
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